An oscillator with mass 2 kg which has the equation of motion 2² +12ª+ 50x = 0 dt where x is the displacement from equilibrium, measured in metres. Answer the following questions a) Which type of oscillator does this equation represent? i)Underdamped oscillator ii)Forced oscillator iii)Critically damped oscillator iv)Undamped Oscillator b) What is the natural frequency of the oscillator? 25 Hz 7.07 Hz 5 Hz 0.79 Hz 0.5 Hz c) If the motion is oscillatory, what is the oscillation time period (choose the nearest answer) 1.36 seconds 1.16 seconds 1.06 seconds 1.26 seconds d) For what value of the damping constant (b) in the unit of kg/s would this system, if displaced, return as quickly as possible to equilibrium? 10 25 5 20
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.
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