Displacement of Oscillating Block: y=A cos(ωt+ø)

In summary, a 5kg block connected to a spring in SHM has a displacement of 15cm at t=0 and reaches its maximum displacement at t=0.3s. The general equation for the displacement is y=A cos (ωt+ø), and with the given information, we can set up two equations to solve for the unknowns. However, a third equation is needed, which should have been the value of the spring constant k. Without it, the problem cannot be solved. If we know the value of k, we can easily solve for the unknowns and find the equation of displacement. Alternatively, we can use the fact that kinetic energy is 0 at the extremes of SHM to find the
  • #1
paulzhen
33
0
A block of 5kg connected to the free end of a spring is hanging from the ceiling and is in SHM. At t=0, the block is traveling upwards and its displacement is 15cm from the equilibrium. The block reaches its maximum displacement 0.3s later. What is the general equation of the displacement of the oscillating block_



y=A cos (ωt+ø)



I use t=0, y=15cm and t=0.3, y=A to get 2 equations:

15=A cosø
0.3ω+ø=0

However there are 3 unknowns in these 2 equations, and I just do not know how to get the 3rd equation from the given quantities. Is this question miss something? Should it tell me the value of force constant k or sth. else? Please help to solve, thanks a lot!

 
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  • #2
They should have given the value of spring constant k.
 
  • #3
lawmaker said:
They should have given the value of spring constant k.

really? is there no way to solve it with all known conditions?
 
  • #4
Kinetic energy is 0 at the extremes in simple harmonic motion.So, Spring constant[itex]\times[/itex]
amplitude[itex]\div[/itex]2=0. This gives you the value of k(spring constant). Now you can solve the problem easily.
 
Last edited:
  • #5
I am so sorry. It is spring constant times the square of the amplitude the whole divided by 2=0
 

1. What is the meaning of the variables in the equation?

The variable y represents the displacement of the oscillating block, which is the distance from its equilibrium position. A represents the amplitude of the oscillation, which is the maximum displacement from the equilibrium position. ω (omega) is the angular frequency, which represents the rate at which the oscillating block moves back and forth. ø (phi) represents the phase shift, which is the horizontal displacement of the oscillating block from the equilibrium position.

2. How does changing the amplitude affect the oscillation?

Increasing the amplitude will result in a larger displacement of the oscillating block from the equilibrium position, making the oscillations more pronounced. On the other hand, decreasing the amplitude will result in smaller oscillations.

3. What does the angular frequency represent?

The angular frequency, ω, represents the rate at which the oscillating block moves back and forth. It is measured in radians per second, and is related to the period of the oscillation (T) by the equation ω = 2π/T. A higher angular frequency means the oscillating block is moving back and forth at a faster rate.

4. How does a phase shift affect the oscillation?

A phase shift, ø, represents the horizontal displacement of the oscillating block from the equilibrium position. It changes the starting point of the oscillation and can make it appear to start at a different position than the equilibrium. A positive phase shift means the oscillating block starts at a position to the right of the equilibrium, while a negative phase shift means it starts at a position to the left of the equilibrium.

5. Can this equation be used to model all types of oscillations?

Yes, this equation can be used to model a wide range of oscillations, including simple harmonic motion and damped oscillations. However, the values of y, A, ω, and ø may vary depending on the specific system being studied.

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