Stuck on harmonic motion question

  • Thread starter PolarClaw
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Hi,

I've been stuck on trying to figure out what im not seeing in the problem as i just cant seem to get the answer.

A particle moving in simple harmonic motion with a period T = 1.5s passes through the equilibrium point at time t initial = 0 with a velocity of 1.0m/s to the right. At a time t later, the particle is observed to move to the left with a velocity of 0.50m/s. What is the smallest value of the time t?

I just cant see what to do :mad: (although i have calculated the angular frequency ( 4(pi)/3).

Thanks in advance.
 

Answers and Replies

  • #2
Andrew Mason
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PolarClaw said:
Hi,

I've been stuck on trying to figure out what im not seeing in the problem as i just cant seem to get the answer.

A particle moving in simple harmonic motion with a period T = 1.5s passes through the equilibrium point at time t initial = 0 with a velocity of 1.0m/s to the right. At a time t later, the particle is observed to move to the left with a velocity of 0.50m/s. What is the smallest value of the time t?

I just cant see what to do :mad: (although i have calculated the angular frequency ( 4(pi)/3).
The position of the particle will be:

[tex]x = A_0sin(\omega t + \phi)[/tex]

Given the initial condition, x = 0 at t = 0, [itex]\phi = 0[/itex]

The speed is given by:

[tex]\dot x = -A_0\omega cos(\omega t) = v_0cos(\omega t)[/tex]

If [itex]\dot x(t_1) = v_1 = -.5v_0[/itex], then what is [itex]cos(\omega t_1)[/itex]?

So from that, you should be able to work out t1.

AM
 
  • #3
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ahh, i had tried that but i differetiated wrong got the answer now thanks.
 

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