3. Below given figure shows a simple oscillator with damping. In this, a mass m is attached to a spring (spring constant k) and a damper with damping force proportional to -bv. The spring and the damper are attached to the walls on the opposite sides of the mass (see Figure). The oscillator can be driven either by moving an attachment point on the damper (Case I) or the end of the spring (Case II). In both cases, the position of the attachment point as a function of time is s(t) = so cos(wat). For BOTH of the above cases, answer each of the following questions. (i). Write the equations of motion of the mass m. (ii). Find the amplitude of steady state solution in terms of given parameters. க m www Can I: Case IT! P 어 Sct) m Figure: Thro ways to drive an osievator
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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