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qUESTIONS

The displacement of an oscillating particle is given by x = asinωt + bcosωt where a, b and ω are constants. Prove that the particle performs a linear S.H.M. with amplitude A = √ (a² + b²)

A particle performing linear S.H.M. of period 2π seconds about the mean position O is observed to have a speed of b √ 3 m/s, when at a distance b (metre) from O. If the particle is moving away from O at that instant, find the time required by the particle, to travel a further distance b.

At what distance from the mean position is the kinetic energy of a particle performing S.H.M. of amplitude 8 cm, three times its potential energy?

The total energy of a body of mass 2 kg performing S.H.M. is 40 J. Find its speed while crossing the centre of the path.

Potential energy of a particle performing linear S.H.M is 0.1 π² x² joule. If mass of the particle is 20 g, find the frequency of S.H.M.

A needle of a sewing machine moves along a path of amplitude 4 cm with frequency 5 Hz. Find its acceleration 1/30 s after it has crossed the mean position.

In SI units, the differential equation of an S.H.M. is d²x/dt² = − 36x. Find its frequency and period.

At what distance from the mean position is the speed of a particle performing S.H.M. half its maximum speed. Given path length of S.H.M. = 10 cm.

The total energy of a particle of mass 200 g, performing S.H.M. is 10⁻² J. Find its maximum velocity and period if the amplitude is 7 cm.

While completing its third oscillation during linear S.H.M., a particle is at -√3/2 A, heading to the mean position. Determine the phase angle.

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