A body of mass `m` is suspended from a spring fixed to the ceiling of an elevator car. The stiffness of the spring is `x`. At the moment `t=0` the car starts going up with an acceleration`w`. Neglecting the mass of the spring , find the law of motion `y(t0` of the body relative to the elevator car if `y(0)-0` and `y(0)=0`. Consider the following two cases `:`
`(a)` `w=const`,
`(b)` `w=alphat, ` where `alpha `is a constant.

A pulley fixed to the ceiling of an elevator car carries a thread whose ends are attached to the loads of masses 3m and m . The car starts gong up with acceleration g//s . Assuming the masses of the pulley and the thread, as well as friction, to be negligible, find the force exerted by the pulley on the ceiling of car.

A body of mass m was suspended by a non-stretched spring, and then set fre without push. The stiffness of the spring is x . Neglecting the mass of the spring , find : (a) the law of motion y(t) , whee y is displacement of the body from the equilibrium position, (b) the maximum and minimum tensions of the spring in the process of motion.

A body of mass m is suspended from a massless spring of natural length l . It stretches the spring through a vertical distance y . The potential energy of the stretched spring is

A spring mass system is hanging from the ceiling of an elevator in equilbrium Elongation of spring is l . The elevator suddenly starts accelerating downwards with acceleration g//3 find. (a) the frequency and (b) the amplitude of the resulting SHM

A pulley fixed to the ceiling of an elevator car carries a thread whose ends are attached to the masses m_(1) and m_(2) . The car starts going up with an acceleration a_(0) . Assuming the masses of the pulley and the thread as well as the friction to be negligible, find: (a) the acceleration of the load m_(1) relative to the elevator shaft and relative to the car (b) the force exerted by the pulley on the ceiling of the car. Given m_(1) gt m_(2) .

A pulley fixed to the ceiling of an elevator car carries a thread whose ends are attached to the masses m_(1) and m_(2) . The car starts going up with an acceleration a_(0) . Assuming the masses of the pulley and the thread as well as the friction to be negligible, find: (a) the acceleration of the load m_(1) relative to the elevator shaft and relative to the car (b) the force exerted by the pulley on the ceiling of the car. Given m_(1) gt m_(2) .