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Free Practice Set for Oscillations . This practice set contains questions that will cover most important topic of JEE Mains /Advance of this chapter. Periodic motion – period, frequency, displacement as a function of time. Periodic functions. Simple harmonic motion (S.H.M.) and its equation; phase; oscillations of a spring -restoring force and force constant; energy in S.H.M. – kinetic and potential energies; Simple pendulum – derivation of expression for its time period; Free, forced and damped oscillations, resonance. Periodic and Oscillatory Motions : The motion which repeats itself after certain time of interval is known as periodic motion. For e.g. motion of a satellite around the planet, uniform circular motion etc. To and fro periodic motions about a fixed point is known as oscillatory motion. Every oscillatory motion is periodic but the converse is not true. The smallest interval of time after which the motion is repeated is called its period, denoted by T. The reciprocal of T gives the number of repetitions that occur per unit time. This quantity is called the frequency of the periodic motion denoted by f. The relation between f and T is given by, f = 1/T. The unit of frequency is s–1 or Hz (hertz). Simple Harmonic Motion : If a particle moves to and fro about a fixed point (equilibrium position) under the application of a force or torque (called restoring force or torque) which is directly proportional to the displacement (linear or angular), directed towards the fixed point, is called simple harmonic motion. The necessary and sufficient condition for the motion to be simple harmonic (linear) is that the force should be directly proportional to the displacement F = –kx . Damped Simple Harmonic Motion : The motion of a simple pendulum, swinging in air, dies out eventually. This is because the air drag and the friction at the support oppose the motion of the pendulum and dissipate its energy gradually. The pendulum is said to execute damped oscillations.