Periodic Motion
• A motion which repeats itself identically after a fixed interval of time, is called a periodic motion. For example - Motion of arms of a clock, orbital motion of the earth around the sun, motion of a simple pendulum etc.
Oscillatory Motion
• A periodic motion taking place to and fro or back and forth about a fixed point is called oscillatory motion. For example - Motion of a simple pendulum. - Motion of a loaded spring etc.
• If a particle oscillates with its own natural frequency without help of any external periodic force. The oscillation is then called damped oscillation.
• When a body oscillates with the help of an external periodic force with a frequency different from natural frequency of the body, then oscillation is called forced oscillation. Simple Harmonic Motion (SHM)
• An oscillatory motion of constant amplitude and of single frequency under a restoring force whose magnitude is proportional to the displacement and always acts towards mean position, is called Simple Harmonic Motion.
Characteristics of SHM
When a particle executing SHM passes through the mean position:
1. No force acts on the particle.
2. Acceleration of the particle is zero.
3. Velocity is maximum.
4. Kinetic energy is maximum.
5. Potential energy is zero.
When a particle executing SHM is at the extreme end, then:
1. Acceleration of the particle is maximum.
2. Restoring force acting on particle is maximum.
3. Velocity of particle is zero.
4. Kinetic energy of particle is zero.
5. Potential energy is maximum.
Simple Pendulum
• A heavy point mass suspended from a rigid support by means of an elastic inextensible string, is called a simple pendulum.
• Time period of a simple pendulum is given by 𝑇 = 2𝜋(√ 𝑙 /𝑔)
• The time period of a simple pendulum of infinite length is 84.6 min. The time period of a second’s pendulum is 2 s. Its length on the earth is nearly 100 cm.
• Acceleration due to gravity decreases with altitude (height) and therefore time period of a pendulum clock will increase and clock becomes slow.
• If the bob of a simple pendulum is suspended from a metallic wire, then the length of the pendulum increases with increase in temperature and therefore its time period also increases.
• A girl is swinging over a swing. If she stands up over the swing, then the effective length of the swing decreases and therefore, the time period of oscillations decreases.
• A pendulum clock cannot be used in a spaceship.
Damped Harmonic Motion
• When there is friction or any other force acting within an oscillating system, the amplitudes of the oscillation decreases over time to this damping force. This is called damped harmonic motion.
Resonant Oscillations
• When a body oscillates with its own natural frequency (V0) with the help of an external periodic force also called forced harmonic motion. And if the frequency (v) provided by the external agent is equal to the natural frequency of the body, the oscillations of the body are called resonant oscillations.
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