Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Is it possible to have dsmped oscillations when a system is at resonance?will dsmped oscillations occur for any values of b and k? Explain
Resonance is known as the phenomenon in which natural frequency of the system is equal to the applied frequency of an external force.
At resonance, the amplitude of vibration is unbounded. That means the amplitude is increasing rapidly and tends to infinity since continuous energy supply from source is given.
Write the expression
Substituting this form gives an auxiliary equation for λ
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