Simple Harmonic Motion & Elasticity, Reference Circle and Energy

Please consider significant figures and draw visual graphics**
Conceptual Questions:
In the figure below, the shadow moves in simple harmonic motion. Where on the shadow’s path is (a) the velocity (v) equal to zero and (b) the acceleration (a) equal to zero?
**Please note that the velocity (v) and acceleration (a) have the same illustration, in this case I just draw the illustration for velocity (not the acceleration. I suggest that after solving for the velocity, replace the velocity with the acceleration **

Additional information for velocity and acceleration
The velocity vx of the ball’s shadow is the x component of the tangential velocity VT of the ball on the reference circle.

Don't use plagiarized sources. Get Your Custom Essay on
Simple Harmonic Motion & Elasticity, Reference Circle and Energy
From $10/Page
Order Essay

–and–

The acceleration ax of the ball’s shadow is the x component of the centripetal acceleration ac of the ball on the reference circle.

A block is attached to a horizontal spring and slides back and forth in simple harmonic motion on a frictionless horizontal surface. A second identical block is suddenly attached to the first block. The attachment is accomplished by joining the blocks at one extreme end of the oscillation cycle. The velocities of the blocks are exactly matched at the instant of the joining. Explain how (a) the amplitude, (b) the frequency, and (c) the maximum speed of the oscillation change.

A particle is oscillating in simple harmonic motion. The time required for the particle to travel through one cycle is equal to the period of the motion, no matter what the amplitude is. But how can this be, since larger amplitude mean that the particle travels further? Explain.

Is more elastic potential energy stored in a spring when the spring is compressed by one centimeter than when it is stretched by the same amount? Explain.
Problems
The Ideal Spring and Simple Harmonic Motion
A hand exerciser utilizes a coiled spring. A force of 89.0 N is required to compress the spring by 0.0191 m. Determine the force needed to compress the spring by 0.0508 m.

A 0.70-kg block is hung from the and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount of the spring stretches from its unstrained length triples. What is the mass of the second block?
Simple Harmonic Motion and the Reference Circle
(Illustrates the concepts pertinent to this problem) 0.80 kg object is attached to one end of a spring, as in the figure below, and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the drawing. With the aid of these data, determine (a) the amplitude A of the motion, (b) the angular frequency ω, (c) the spring constant K, (d) the speed of the object at t = 1.0 s, and (e) the magnitude of the object’s acceleration at t = 1.0 s.

2.0 4.0
1.0 3.0

A person bounces up and down on a trampoline, while always staying in contact with it. The motion is simple harmonic motion, and it takes 1.90 s to complete one cycle. The height of each bounce above the equilibrium position is 45.0 cm. Determine (a) the amplitude and (b) the angular frequency of the motion. (c) What is the maximum speed attained by the person?
Energy and Simple Harmonic Motion
An archer pulls the bowstring back for a distance of 0.47 m before releasing the arrow. The bow and the string acts like a spring whose spring constant is 425 N/m. (a) What is the elastic potential energy of the drawn bow? (b) The arrow has a mass of 0.0300 kg. How fast is it traveling when it leaves the bow?

A spring is hung from the ceiling. 0.045 kg block is then attached to the free end of the spring. When released from rest, after which it moves back upward. (a) What is the spring constant of the spring? (b) Find the angular frequency of the block’s vibrations.

A rifle fires a 2.10 x 10-2 kg pellet straight upward, because the pellet rests on a compressed spring that is released when trigger is pulled. The spring has a negligible mass and is compressed by 9.10 x 10-2 m from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.

A vertical spring with a spring constant of 450 N/m is mounted on the floor. From directly above the spring, which is unstrained, a 0.30 kg block is dropped from rest. It collides with and sticks to the spring, which is compressed by 2.5 cm in bringing the block to a momentary halt. Assuming air resistance is negligible; from what height (in cm) above the compressed spring was the block dropped?

A 3.2 kg block is hanging stationary from the end of a vertical spring that is attached to the ceiling. The elastic potential energy of the spring/mass system is 1.8 J. What is the elastic potential energy of the system when the 3.2 kg block is replaced by a 5.0 kg block?

A 1.00 x 10-2 kg block is resting on a horizontal frictionless surface and is attached to a horizontal spring whose spring constant is 124 N/m. The blocked is shoved parallel to the spring axis and is given an initial speed of 8.00 m/s. while the spring is initially unstrained. What is the amplitude of the resulting simple harmonic motion? Solution Preview
**Please consider significant figures and draw visual graphics**
Conceptual Questions:
 In the figure below, the shadow moves in simple harmonic motion. Where on the shadow’s path is (a) the velocity (v) equal to zero and (b) the acceleration (a) equal to zero?
**Please note that the velocity (v) and acceleration (a) have the same illustration, in this case I just draw the illustration for velocity (not the acceleration. I suggest that after solving for the velocity, replace the velocity with the acceleration **

Additional information for velocity and acceleration
 The velocity vx of the ball’s shadow is the x component of the tangential velocity VT of the ball on the reference circle.

–and–

 The acceleration ax of the ball’s shadow is the x component of the centripetal acceleration ac of the ball on the reference circle.

Answer: a) Velocity v is zero at the extreme positions of the shadow i.e. x = + radius of the circular path.

b) Acceleration a is zero at the position x = 0.

 A block is attached to a horizontal spring and slides back and forth in simple harmonic motion on a frictionless horizontal surface. A second identical block is suddenly attached to the first block. The attachment is accomplished by joining the blocks at one extreme end of the oscillation cycle. The velocities of the blocks are exactly matched at the instant of the joining. Explain how (a) the amplitude, (b) the frequency, and (c) the maximum speed of the oscillation change.

Solution: a) Amplitude of oscillations remains unchanged because the second mass is attached at the extreme position where the speeds of the two blocks are zero. Hence, second block does not add any mechanical energy to the system.
___
b) Frequency of oscillations is given by: ν = (1/2П)√k/m

With doubling of mass, frequency will reduce by a factor of 1/√2 = 0.707

c) The second block is attached to the first one at one of the extreme ends where the velocity is zero. As the blocks now move towards the mean position, the elastic PE of the spring is converted into the KE of the blocks. As the mass has doubled and the KE remains unchanged (equal to maximum PE of the spring), let the speed at the mean position be v2. Then, ½ mv12 = ½ (2m) v22 where v1 = speed of the single mass at the mean position

v12 = 2v22 or v2 = v1/√2 = 0.707 v1

Maximum speed reduces by a factor of 0.707.

 A particle is oscillating in simple harmonic motion. The time required for the particle to travel through one cycle is equal to the period of the motion, no matter what the amplitude is. But how can this be, since larger amplitude mean that the particle travels further? Explain.

Answer: With larger amplitude, the particle travels faster i.e. it has a greater speed at any given point. Hence, the larger distance is travelled at higher speed maintaining the time period constant.

 Is more elastic potential energy stored in a spring when the spring is compressed by one centimeter than when it is stretched by the same amount? Explain.

Answer: Elastic PE stored in …

Solution Summary
Simple harmonic motion and elasticity is examined. Reference circle and energy are provided.To continue with the answer check on mycoursewriter.com/

MyCourseWriter
Order NOW For A 35% Discount!
Pages (550 words)
Approximate price: -

Why Choose Us

Quality Homework Writing

Do you need to ace your test? We have qualified writers to assist you in writing 100% quality homework writing. Mycoursewriter offers students unique and personalized custom papers that help them in getting good grades. Our academic experts will assist you with your dissertation papers, thesis writing, research papers, term papers, and case study homework help. Our writers are experienced and have perfected the art of crafting the best essay writing papers regardless of your academic level. Order now and get our superb homework writing services.

Expert Academic Writers

A student needs professional assistance outside class time. Before hiring our writers, they undergo thorough tests and strict educational backgrounds. After passing a test, our writers undergo training to ensure they deliver expert professional papers to our customers. We ensure they meet the timely delivery of papers and follow our customers' provided instructions. Every writer is an ENL writer and is from the USA, Canada, UK, or Australia. Our experts approach papers effectively depending on their area of specialization.

Affordable Price Guarantees

Is the deal too good to be true? Mycoursewriter is the most affordable assignment help website on the market. We consider students' daily needs for academic help. Our paper costs are reasonably priced to approximately 90% of students around the globe. Our main aim is to ensure students achieve academic excellence, and we believe inconsiderable prices should not hinder students from getting quality homework writing help. In case of any dissatisfaction, we offer unlimited revisions and rewrites without extra charges.

Timely delivery of papers

Tight deadline? Is your paper due in the next few hours? Worry no more. Our writers are here for your rescue. Many college students find it hard to balance their social and academic life and get caught up with academic deadlines. Drafting your paper at the last minute does not allow you to conduct extensive research and craft the correct answers. We have expert writers ready to work on your assignment writing. Urgent writing services are the ultimate solutions you need. We guarantee you timely delivery of papers at your convenience and specified time delivery of the customer.

100% Original Tasks

The ultimate deal-breaker in achieving good grades is submitting imitative papers. Plagiarism is a breach of examination standards and has serious consequences. Students need to deliver papers written in their understanding by paraphrasing their research findings and relevant citations. Our expert's primary consideration is providing free plagiarized papers that meet the lecturers' requirements. Our editors will proofread your paper before delivery ad ensure your papers will not be substandard. We guarantee extreme originality, and in case of any customer concerns, we offer a plagiarism report.

All Round the clock Customer Support

Our website is user-friendly and super useful! Mycoursewriter is the most trusted online writing website always available to provide you with assignment writing services that you need. Our primary concern is meeting customer need specifications by our friendly customer support team that Is available all the time. Our website usability is self-learnable but in case of any problem, feel free to contact us directly through our website email: support@mycourserwiter.com. We have diligently satisfied thousands of students, and you can witness this on our sites' review page.

Try it now!

Calculate the price of your order

We'll send you the first draft for approval by at
Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Advantages of Using Our Assignment writing Services

Mycoursewriter welcomes you for superb essay writing services. We are a legit site offering help with your most challenging homework writing assignments at affordable prices. Your essay paper will be assigned to a professional writer who will craft the paper from scratch according to your provided instructions.

Essays

Essay Writing and Proofreading Services

Essay writing is a common assignment writing for most college students. It takes a lot of time to craft a complete perfect essay. Mycourserwiter offers the best essay writing and proofreading services for most college students. Your paper is assigned to an expert writer who does thorough research on fresh ideas and personalizes your essay paper according to your assignment writing guidelines. Our essays are entirely exceptional and undergo a strict procedure that includes papers free from plagiarism and thorough proofreading.

Admissions

Admission and Business Papers

Writing an admission paper is not every student's desire, and this should not hinder any student from earning an admission. Writing a perfect personal statement to earn a position in a dream school or job can be stressful. Personal statements should display a high level of confidence and uniqueness. Admission essays require you to have a vast knowledge of the current happenings in the world and knowhow of the business world. We have qualified writers with skills who will write your admission paper through comprehensive research. All you have to do is provide us with little details about yourself, instructions and our writers will craft a perfect paper for you.

Editing

Editing and Proofreading

Mycoursewriter offers you assignment writing services free from grammatical and formatting mistakes. An error-free paper is significant in scoring the desired maximum grades. We have a team of editors who will go through your paper after our expert writers have delivered their fully crafted papers. Our writers will cover all the aspects of your paper instructions, such as fonts, spacing, and educational formats. Our team of editors will check through your paper to make sure it meets the formatting style provided in the paper instructions. Under no circumstances will a poorly formatted paper will be forwarded to you as our team of editors will ensure careful proofreading.

Coursework

Technical Papers

Assignment writing is part of a learning process, and one may not have the knowledge to answer all questions correctly. This should not be a stress to you as we have qualified essay writing experts to help you. Our qualified writers are holders of PhDs, Degrees, and Masters in different areas of study and can handle any papers regardless of the complexity. Multiple assignments may be challenging to finish on time. Our skilled professional writers are here to assist you in crafting all the correct answers for your assignment. Stop stressing about your homework writing and place an order with us, and our expert writers will provide you with the best assignment help.