Given

Acceleration due to gravity on the surface of moon, g^{’ }= 1.7 m s^{-2}

Acceleration due to gravity on the surface of earth, g = 9.8 m s^{-2}

Time period of a simple pendulum on earth, T = 3.5 s

T = 2 π\( \sqrt{\dfrac{I}{g}}\)

Where,

l is the length of the pendulum

Therefore,

l = \( \dfrac{T^2}{(2 π)^2}\) x 2

On substituting, we get,

l = \( \dfrac{3.5^2}{(4 \times (3.14))^2}\) x 9.8 m

The length of the pendulum remains constant

On moon’s surface, time period, T^{’} = 2 π\( \sqrt{\dfrac{I}{g}}\)

= 2 π \( \sqrt{\dfrac{(3.5)^2}{\dfrac{4 \times (3.14)^2 \times 9.8}{1.7}}}\)

We get,

= 8.4 s

Therefore, the time period of the simple pendulum on the surface of the moon is 8.4 s

Answered by Pragya Singh | 1 year agoA mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x_{0} and pushed towards the centre with a velocity v_{0} at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, x_{0} and v_{0}. [Hint: Start with the equation x = a cos (ωt+θ) and note that the initial velocity is negative.]

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is

**(a)** 5 cm

**(b)** 3 cm

**(c)** 0 cm.

A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant α is defined by the relation J = –α θ, where J is the restoring couple and θ the angle of twist).

Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

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**(a)** the spring constant k and

**(b)** the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 750 kg.