As a spring is heated, its spring "constant" decreases. Suppose the spring is heated so that the spring "constant" at time t is k(t)=9-t N/m. If the unforced mass-spring system has mass m = 2 kg and a damping constant b=1 N-sec/m with initial conditions x(0) = 4 m and x'(0) = 0 m/sec, then the displacement x(t) is governed by the initial value problem 2x'' (t) + x'(t) + (9-t)x(t) = 0; x(0) = 4, x'(0) = 0. Find the first four nonzero terms in a power series expansion about t=0 for the displacement. CU k(t)=9-t გგგგგგ heat 2 kg 1 N-sec/m x(t) x(0) = 4 x'(0)=0
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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