Maximum Velocity When Doubling Amplitude & Period of SHM

[adrian783]

what happens to the maximum velocity if you double both Amplitude and period of a SHM?

the equation is

x(t) = A cos (wt + f)
v(t) = -A w sin (wt + f)

f is phase constant, w = angular velocity

i know if i double A and T, the first part of the v(t) equation will be like:
-2A * 2pi/2T = -A * w, not changed, but what about that part in the sine ?

the question ask if it is halved, quadrupled, unchanged, or doubled

 

[dextercioby]

You're asked about the maximum velocity.That should happen when the sine is either +1 or -1 (abosolute value,nevermind the sense)...Therefore,it's not a factor to this problem...


Daniel.

 

[thepatientmental]

If you double both the amplitude (A) and the period (T) of a simple harmonic motion (SHM), the maximum velocity will remain unchanged. This can be seen by plugging in the new values into the equation for velocity (v = -Aωsin(ωt + φ)). The first part of the equation, -Aω, will remain the same since the amplitude is doubled and the angular velocity (ω) is halved. However, the second part of the equation, sin(ωt + φ), will also remain the same since the period is doubled, resulting in the same value for ωt + φ. Therefore, the maximum velocity will not be affected and will remain the same as before.