Question

A particle that hangs from a spring oscillates with an angular frequency of 2 rad/s. The spring particle system is suspended from the ceiling of an elevator car and hangs motionless (relative to the elevator car) as the car descends at a constant speed of 1.5 m/s. The car then stops suddenly. With what amplitude does the particle oscillate?

• A. $0.75m$
• B. $0.95m$
• C. $1.75m$
• D. $0.56m$

Answer 1

The correct option is A $0.75m$

When travelling in the elevator at a constant speed,the total force on mass is zero.The force exerted by spring is equal to in magnitude to the gravitational force on the mass,the spring has equilibrium length equal to its own length . At moment elevator stops spring touches elevator stops and the mass with acquired a momentum mv which streaches it .The max velocity $u_{max}=1.5m/s$

The equation of velocity of mass.

$v.\left(t\right)=-\omega A\sin (\omega ++\varphi )$

So,$\left|v_{max}\right|=\omega A$ $\omega$ = 2 rad/s given

A=$\frac{v_{max}}{\omega }=\frac{1.5}{2}=0.75$ meter