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If the damping in the case of a damped harmonic oscillator be very small, obtain expressions for (i) average total energy of the oscillator, and (ii) average rate of energy dissipation. Also show that the average rate of energy dissipation is equal to the work done by the damping for per second.
An underdamped harmonic oscillator has its amplitude reduced to 1/10 th of its initial value after 100 oscillations. If the time period be 1.15 sec, calculate the time in which (i) its amplitude, and (ii) energy falls to 1/e th of its undamped value. If the mass of the oscillator be 1.127 gm, calculate its average rate of loss of energy.
Discuss analytically the theory of forced vibrations in the presence of damping force proportional to the velocity of the vibrating particle and obtain the condition of resonance. Explain the quality factor, and sharpness of resonance and the factors on which they depend.

A 0.58-kg basket falls from a height of 7.7 m. How much work is done by gravity on the ball?


weight=900N on the earth what is weight on Jupiter where the acceleration due to gravity is 25.9m/s^2


Dot or Scalar Product

1. Calculate the dot product of vectors a and b where a is 4 units and b is 8 units and angle Theta is 67
Dot or scalar Product

1. Calculate the dot product of vectors a and b where a is 4 units and b is 8 units and angel theta is 67
A 40,000 kg jet plane flies at a speed around 550 mph. ignoring any gravitational forces, What is the net force on the jet plane?



Give 2 situation wherein static is applicable in our lives.
Give 2 situations wherein kinetic friction is applicable in our lives.

A wooden disc of 2 m radius and 120 kg mass rotates through a vertical axis at the

centre of the disc. Later a 100 kg bag containing sand is released vertically onto the disc

at a point near the side of the disc. (o = 3 rad s-1)


Calculate the


(a) moment of inertia of the disc. [3 m]

(b) angular velocity after the sand bag is released (assume that the sand bag is a

particle).


A pulley is mounted on a frictionless axis and then the pulley is attached to the

higher end of the inclined surface as shown in the figure. A massless cord is

wrapped around the pulley while its other end is tied to a 1.0 kg object. The pulley

has a radius of 20 cm and moment of inertia of 0.4 kg m2


. The angle of the surface

is 37° and the coefficient of kinetic friction is 0.2. The object is released from

rest. The pulley starts to rotate as the object moves and the cord unwinds.

Determine the acceleration of the object and the tension in the cord.


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