Question

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?

Answer 1

Concept :- in SHM , maximum speed is at the mean position when acceleration of particle is minimum. Whereas maximum acceleration is at either of extreme position speed is minimum.

Here,
angular frequency ( w) = 200 rad/Mon
stroke length = 1 m
Amplitude of SHM,
A = stroke length/2
= 1/2 = 0.5 m

Now,
Vmax = wA
= 200 × 0.5 = 100 m/min