An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical spring of spring constant k = 85 N/m, the effect of the fluid resistance is governed by the damping constant b = 0.07kg/s. (i) Find the period of the damped oscillation. (ii) How long does it take for the amplitude of the damped oscillation to drop to half of its initial value?
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.
An object of mass m = 0.25 kg oscillates in a fluid at the end of a vertical
spring of spring constant k = 85 N/m, the effect of the fluid resistance is governed by the damping constant b = 0.07kg/s.
(i) Find the period of the damped oscillation.
(ii) How long does it take for the amplitude of the damped oscillation to drop to half of its initial value?
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