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Let the equation of oscillation be given by  Velocity would be given as  Kinetic energy at an instant is given by Time Period  is given by The Average Kinetic Energy would be given as follows The potential energy at an instant T is given by  The Average Potential Energy would be given by We can see Kav = Uav
At the maximum extension of spring, the entire energy of the system would be stored as the potential energy of the spring. Let the amplitude be A The angular frequency of a spring-mass system is always equal to  Therefore
A = 5 cm = 0.05 m T = 0.2 s At displacement x acceleration is  At displacement x velocity is  (a)At displacement 0 cm
A = 5 cm = 0.05 m T = 0.2 s At displacement x acceleration is  At displacement x velocity is  (a)At displacement 3 cm
A = 5 cm = 0.05 m T = 0.2 s At displacement x acceleration is  At displacement x velocity is  (a)At displacement 5 cm
Moment of Inertia of the disc about the axis passing through its centre and perpendicular to it is The period of Torsional oscillations would be
The amplitude of oscillation decreases by 50 % in one oscillation i.e. in one time period. For damping factor b we have   x=x0/2 t=0.77s m=750 kg
Mass of automobile (m) = 3000 kg There are a total of four springs. Compression in each spring, x = 15 cm = 0.15 m Let the spring constant of each spring be k
Let the initial volume and pressure of the chamber be V and P. Let the ball be pressed by a distance x. This will change the volume by an amount  ax. Let the change in pressure be  Let the Bulk's modulus of air be K. This pressure variation would try to restore the position of the ball. Since force is restoring in nature displacement and acceleration due to the force would be in different...
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