Simple Harmonic motion and collisions

In summary: I'm not sure if that will work either...A block of mass 2kg oscillates on the end of a spring in SHM with a period of 20ms. The position of the block is given by: x=(1.0cm)cos(wt+2pi). If the position is given by:x=(1.0cm)cos(wt+2pi) then, t=5.0ms corresponds to an angle of pi/2. The velocity equation is:v=-w(1.0cm)sin(wt+2pi). v does not equal 0 at t=5.0ms.I'd do part b first to get the
  • #1
cherylsc
2
0
A block of mass 2kg oscillates on the end of a spring in SHM with a period of 20ms. The position of the block is given by: x=(1.0cm)cos(wt+2pi). Another block of mass 4kg slides toward the oscillating block with velocity of 6m/s. The two blocks undergo a completely inelatic collision at time t=5.0ms.

a)what is the amplitude of oscllaltion after collision?
I know momentum is conserved in the collision and time t=.005 secons, the velocity of the oscillating block is O. So I got V(final)=4m/s.
But I am not sure how to account for this with the spring force to get the final amplitude.

b) What is the frequency of the resulting SHM?
without A, I don't think I can do this part, so I haven't tried yet...
 
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  • #2
cherylsc said:
A block of mass 2kg oscillates on the end of a spring in SHM with a period of 20ms. The position of the block is given by: x=(1.0cm)cos(wt+2pi).

Are you sure it's cos(wt+2pi)? Might as well make it cos(wt).

Another block of mass 4kg slides toward the oscillating block with velocity of 6m/s. The two blocks undergo a completely inelatic collision at time t=5.0ms.

a)what is the amplitude of oscllaltion after collision?
I know momentum is conserved in the collision and time t=.005 secons, the velocity of the oscillating block is O. So I got V(final)=4m/s.

If the position is given by:
x=(1.0cm)cos(wt+2pi) then, t=5.0ms corresponds to an angle of pi/2. The velocity equation is:
v=-w(1.0cm)sin(wt+2pi). v does not equal 0 at t=5.0ms.

I'd do part b first to get the new w... then use the fact that the magnitude of the maximum velocity = wA. Since you have the maximum velocity (you get it from the conservation of momentum etc...) you can get A (amplitude).

But I am not sure how to account for this with the spring force to get the final amplitude.

b) What is the frequency of the resulting SHM?
without A, I don't think I can do this part, so I haven't tried yet...

w=sqrt(k/m).

You can calculate k, then solve for the new w using a mass of 6kg
 
  • #3
oops

I meant (1/2)pi

thanks
 

1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium position. It occurs when the restoring force on the object is directly proportional to its displacement from the equilibrium position and is directed towards that position.

2. What factors affect the period of a simple harmonic motion?

The period of a simple harmonic motion is affected by two main factors: the mass of the object and the stiffness of the spring or medium that is providing the restoring force. A larger mass or a stiffer spring will result in a longer period of oscillation.

3. How is simple harmonic motion related to circular motion?

Simple harmonic motion can be thought of as a projection of circular motion onto a straight line. This is because the motion of an object undergoing SHM can be described using the same equations as those used to describe uniform circular motion, with the displacement representing the position on the circle and the velocity representing the tangential velocity.

4. What is the difference between elastic and inelastic collisions?

Elastic collisions are collisions in which both kinetic energy and momentum are conserved, meaning that the total energy and momentum of the system before and after the collision remain the same. Inelastic collisions, on the other hand, are collisions in which some kinetic energy is lost and the total energy of the system decreases.

5. How do collisions affect the period of a simple harmonic motion?

Collisions can affect the period of a simple harmonic motion by changing the mass or stiffness of the system. In an elastic collision, the period will remain the same as the total energy and momentum are conserved. In an inelastic collision, the period may change depending on the amount of energy lost during the collision.

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