SHM Question (1 Viewer)

[Smilebuffalo]

SHM.

Find the maximum speed of a particle moving in SHM, if its displacement is given by x = 5cos3t + 2sin3t

answer: 16.2m/s

Is there any particular method that i'm meant to use in SHM for this question?

 

[Pwnage101]

use auxiliary angle method to write in form x= Rsin(t+b), and you know maximum speed is when acceleration is zero, which is when displacement is zero, so find whenever that is and sub that value of t back into velocity.

 

[Trebla]

SHM.

Find the maximum speed of a particle moving in SHM, if its displacement is given by x = 5cos3t + 2sin3t

answer: 16.2m/s

Is there any particular method that i'm meant to use in SHM for this question?

Alternatively, find it by inspection:
v = dx/dt
= -15 sin 3t + 6cos 3t
= Rsin (3t + a)
the maximum of v = Rsin (3t + a) clearly occurs when sin (3t + a) = 1, in other words when v = R
But:
R = √(15² + 6²) ~ 16.2
Hence
v_max ~ 16.2 m/s