Simple Harmonic Motion of a cart

In summary: The cart oscillates back and forth in simple harmonic motion.The cart is 0.182 meters from the spring's equilibrium position when it's moving with a speed of 1.00 m/s.
  • #1
biomajor009
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0

Homework Statement


A 0.620-kg cart is moving down an air track with a speed of 2.33 m/s when it collides with a spring. The spring is initially at its equilibrium position, but the cart compresses the spring. It takes 0.0780s after the cart hits the spring for the cart to come to a stop. The cart then remains attached to the spring and oscillates back and forth in simple harmonic motion.
(a) What is the period of this oscillation?
(b) Find the force constant of the spring.
(c) What is the amplitude of the oscillation?
(d) What is the maximum acceleration experienced by the cart as it oscillates?
(e) How far is the cart from the spring’s equilibrium position when it is moving with a speed of 1.00m/s?

Homework Equations


x = Acos([tex]\omega[/tex]t)
v = −A[tex]\omega[/tex]sin([tex]\omega[/tex]t)
a = −A[tex]\omega[/tex]^2cos([tex]\omega[/tex]t)

The Attempt at a Solution


I don't know how to find the period without angular velocity, and I'm not sure how to find the angular velocity with the information I have. I did find the force constant to 101.8N/m using conservation of energy, which then allowed me to find the amplitude to be 0.182m. But the rest have me confused because I'm not sure how to find angular velocity with the information I have. I could determine it with the force constant since [tex]\omega[/tex]=[tex]\sqrt{}k/m[/tex] but I'm supposed to find period without knowing the force constant
 
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  • #2
Are you sure k is correct? How did you find it? I have no calculator to hand (don't like the compueter one...and it's late, but I don't think 101.8 is correct, but I may be doing it wrong in my head - it is VERY late!)

The mass hits the spring in equilibrium position and then comes to a stop 0.0780 seconds later...what fraction of an oscillation does that represent?

Then use the period to calculate the spring constant...

Hope that helps
 
  • #3
biomajor009 said:

I don't know how to find the period without angular velocity, and I'm not sure how to find the angular velocity with the information I have.


It takes 0.0780s after the cart hits the spring for the cart to come to a stop.Then it takes 0.0780s after the cart stops for the cart to come back.It's half of one complete oscillation.
 

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion in which an object oscillates back and forth between two points, with a constant amplitude and frequency. It is often described as the motion of a mass attached to a spring that is stretched or compressed.

2. How does a cart exhibit Simple Harmonic Motion?

A cart can exhibit Simple Harmonic Motion when it is attached to a spring and allowed to move freely on a horizontal surface. The spring provides a restoring force that causes the cart to oscillate back and forth in a repetitive pattern.

3. What factors affect the period of a cart's Simple Harmonic Motion?

The period of a cart's Simple Harmonic Motion is affected by the mass of the cart, the stiffness of the spring, and the amplitude of the motion. The period is directly proportional to the mass and inversely proportional to the stiffness and amplitude.

4. How is the displacement of a cart related to its Simple Harmonic Motion?

The displacement of a cart in Simple Harmonic Motion is directly proportional to the force exerted by the spring. As the cart moves away from its equilibrium position, the spring exerts a restoring force that brings the cart back to its starting point. The displacement is also affected by the amplitude and frequency of the motion.

5. What are some real-life examples of Simple Harmonic Motion?

Some common examples of Simple Harmonic Motion include the motion of a pendulum, a mass attached to a spring, and the swinging motion of a child on a swing. The motion of a vibrating guitar string and the motion of a car's suspension system can also be described as Simple Harmonic Motion.

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