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The damping force is proportional to the velocity and acts against the direction of motion (FD=−bv).

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The damping force is proportional to the velocity and acts against the direction of motion (FD=−bv).

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The only contribution of the weight is to change the equilibrium position

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The only contribution of the weight is to change the equilibrium position

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Elastic potential energy which is stored in the spring;
Pendulum converts potential energy to kinetic energy over and over

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During the oscillations, the total energy is constant and equal to the sum of the potential energy and the kinetic energy of the system, ETotal=12kx2+12mv2=12kA2.

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During the oscillations, the total energy is constant and equal to the sum of the potential energy and the kinetic energy of the system, ETotal=12kx2+12mv2=12kA2.

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At maximum displacement from the equilibrium point, potential energy is a maximum while kinetic energy is zero. At the equilibrium point the potential energy is zero and the kinetic energy is a maximum. 

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At maximum displacement from the equilibrium point, potential energy is a maximum while kinetic energy is zero. At the equilibrium point the potential energy is zero and the kinetic energy is a maximum. 

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The reduction in amplitude (or energy) of an oscillator is called damping and the oscillation are said to be damped.
oscillations, the energy (and hence the amplitude) of which decreases with time. The damping of free mechanical harmonic oscillations is associated with a decrease in mechanical energy due to the action of resistance and friction forces.

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Damped oscillations are not a truly periodic process, since they never repeat the values ​​of physical quantities.

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Без названия

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The energy transported by a wave is directly proportional to the square of the amplitude

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Critical damping reduces the amplitude of the oscillations to zero in the shortest possible time, returning the system to the equilibrium point. Heavy damping returns the system to the equilibrium point slowly with no full oscillation.

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Critical damping reduces the amplitude of the oscillations to zero in the shortest possible time, returning the system to the equilibrium point. Heavy damping returns the system to the equilibrium point slowly with no full oscillation.

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The total energy remains constant, but the energy oscillates between kinetic energy and potential energy. When the kinetic energy is maximum, the potential energy is zero

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Damping is the presence of frictional or resistive forces which dissipate energy (mechanical energy is converted into thermal energy)​

The amplitude of the oscillations decreases with time​

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Critical damping reduces the amplitude of the oscillations to zero in the shortest possible time, returning the system to the equilibrium point. Heavy damping returns the system to the equilibrium point slowly with no full oscillation

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For instance, they reduce the amplitude of vibrations during an earthquake. When a building sways in one direction during an earthquake, the motion of the damper lags behind. After a few cycles, the damper is moving in the opposite direction as the building, and this reduces the overall sway.

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 As the object starts to move, the elastic potential energy is converted into kinetic energy, becoming entirely kinetic energy at the equilibrium position. The energy is then converted back into elastic potential energy by the spring as it is stretched or compressed.

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 As the object starts to move, the elastic potential energy is converted into kinetic energy, becoming entirely kinetic energy at the equilibrium position. The energy is then converted back into elastic potential energy by the spring as it is stretched or compressed.

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If δ > ω0, then the friction in the system is very high and no oscillations occur, the stock of mechanical energy of the body by the time it returns to the equilibrium position is completely spent on overcoming friction.

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Безымянный5555

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Damping

Any completely isolated system exhibiting simple harmonic motion will carry on swinging/vibrating forever! It conserves mechanical energy. There will be continuous interchange of kinetic to potential energy and back again.

For example,

In a spring-mass system, the energy conversion is between kinetic energy and the potential energy stored in a stretched or compressed spring.
In a pendulum, the energy is converted between kinetic energy and gravitational potential energy.