Subjective Question for SHM

Q1. A mass attached to a spring is free to oscillate , with angular velocity ω , in a frictionless horizontal plane. The mass is displaced from it's equilibrium position by a distance x0 towards the center by pushing it with velocity v0 at time t=0. Find the amplitude of resulting oscillations in terms ofω,x0 and v0 .
Ans. A=√[x02+(v022)]


Q2. A uniform cylinder of length l and mass m having crosssectional area Ais suspended , with length vertical , from a fixed point by a massless spring , such that it is half submearged in a liquid of density σ at equilibrium position.. When the cylinder is given a small downward push and released , it starts oscillating verticallywith small amplitude . Calculate the frequency of oscillations of cylinder.
(IIT 1990)
Ans. f=[(k+(σAg)/m]1/2


Q3. What should be the percentage change of length of pendulum in order that clock have same time period when moved from place where g=9.8 m/s2 to another where g=9.81 m/s2.
Ans. .102%

Q4. A 4 kg particle is moving along x axis under the action of the force F=-(π2/16)x N
when t=2 s the particle passes through origin.If x0 is the amplitude of oscillating particle find the equation of elongation.
Ans. x=x0 cos( πt/8 + π/4)


Q5. Two blocks of masses m1 and m2 are connected by a spring and these masses are free to oscillate along the axis of the spring. Find the angular frequency of oscillation.
Ans.
ω=√[k(m1+m2)/m1m2]

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