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 x

Ans. A=√[x

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]

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/s

Ans. .102%

Q4. A 4 kg particle is moving along x axis under the action of the force F=-(π

when t=2 s the particle passes through origin.If x

Ans. x=x

Q5. Two blocks of masses m

Ans.

ω=√[k(m

_{0}towards the center by pushing it with velocity v_{0}at time t=0. Find the amplitude of resulting oscillations in terms ofω,x_{0}and v_{0}.Ans. A=√[x

_{0}^{2}+(v_{0}^{2}/ω^{2})]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/s

^{2}to another where g=9.81 m/s^{2}.Ans. .102%

Q4. A 4 kg particle is moving along x axis under the action of the force F=-(π

^{2}/16)x Nwhen t=2 s the particle passes through origin.If x

_{0}is the amplitude of oscillating particle find the equation of elongation.Ans. x=x

_{0}cos( πt/8 + π/4)Q5. Two blocks of masses m

_{1}and m_{2}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(m

_{1}+m_{2})/m_{1}m_{2}]
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