Another SHM Question (1 Viewer)

[nofate]

A particle moves in simple harmonic motion with acceleration = -49x. Initially the particle is 1m to the right of the origin.
a) Find the period of the motion (easy)
b) Find the maximum speed of the particle (I have no idea how to do this)
c) Find the times when the displacement is 0.5m (Haven't attempted since haven't done part b).

 

[Sy123]

Is that the whole question, because for part b, the max speed occurs at the centre of oscillation (equilibrium), which is at x=0 according to acceleration=-49x
So what I have attempted to do is integrate using (1/2 v^2)d/dx = -49x
However we have no information to find +C
Because we dont know what the velocity is at x=1 (the only information we have)

 

[Alex_Germ]

Assume it starts at an end point.

x= cos(7t)

dx/dt = -7sin(7t)

Max velocity occurs when sin(7t)=-1

Max V = 7m/s

 

[Sy123]

So we can assume that it starts at the end point?

I dont think you can.

 

[Alex_Germ]

So we can assume that it starts at the end point?

I dont think you can.

A genius like me can.

They really should specify the question more, but it still makes no difference. It's doesn't matter where the thing starts, it will still have the same max speed. The phase angle doesn't change the max speed it gets.

 

[nofate]

Yep that was the whole question. My teacher assumed that it started at an endpoint, but was also under the belief that assuming that fact was incorrect.