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What do you understand by damped oscillations?

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If there is only restoring force acting on a vibrating object for example simple pendulum or tuning fork then that object can vibrate till infinity. This type of vibration or oscillation is called ‘free oscillation’ and this type of vibration is called ‘free vibration’. Its frequency is called ‘Natural Frequency’. There is only restoring force working in free vibration. Its amplitude and energy both are constant with time.

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