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College Physics (Urone)
Found in: Page 588

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Short Answer

Explain in terms of energy how dissipative forces such as friction reduce the amplitude of a harmonic oscillator. Also, explain how a driving mechanism can compensate. (A pendulum clock is such a system.)

Dissipative force such as friction absorbs the energy of the harmonic oscillator and as a result, reduces its amplitude.

In the driving mechanism, the external force provides energy to compensate for the energy loss due to dissipative forces.

See the step by step solution

Step by Step Solution

Step 1: Definition of the dissipative forces

The forces that are concerned with energy loss are called dissipative forces. The loss of energy takes place in the system when the system is in motion.

Step 2: Determination of the fact that how dissipative forces impact the total energy and amplitude of an oscillator

A simple harmonic oscillator has no dissipative forces and so its total energy remains constant. The energy oscillates back and forth between kinetic energy and potential energy such that the sum of these energies remains constant.

It is expressed as follows,

K.E + P.E = T.E

Here, K.E is the kinetic energy, P.E is the potential energy, and T.E is the total energy.

This is in accordance with the law of conservation of energy.

In the case of a harmonic oscillator the total energy is given as follows,

\(T.E = \frac{1}{2}k{A^2}\)

Here K is the force constant and A is the amplitude of oscillation.

When dissipative forces act on the system, they tend to remove energy from the system, usually in the form of thermal energy. Since Energy is directly proportional to the square of the amplitude. So, due to the decrease in the total energy of the system, the amplitude gets reduced.

Step 3: Determination of the fact that how a driving mechanism can compensate 

In the driving mechanism, the external forces act on the system to compensate for the dissipative forces such as friction. The external force also makes up for the energy loss by providing extra energy to keep the total energy of the oscillation constant throughout.

As a result, the amplitude also remains constant throughout even though dissipative forces remain present.

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