Question

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

Answer 1

Answer:

now the stroke is twice the amplitude of the simple harmonic motion.

so the amplitude,a=1/2m=0.5m

angular frequency of oscillation, w=200

rad/min=200/60=10/3 rad/s

we know for a body undergoing simple harmonic motion the velocity is maximum when the body is at mean position or middle position and maximum velocity is given by relation ,v = aw

where a is the amplitude and w is the angular frequency of oscillation

so, we get maximum velocity of position as v= 0.5m*10/3=5/3m/s=1.67m/s.

so, we get maximum velocity of the position is 1.67 m/s.