The bob on a simple pendulum is pulled to the left 4 in. from its equilibrium position. After release, the pendulum makes one complete back-and-forth cycle in 2 sec and follows simple harmonic motion. a) Write a function to model the displacement d (in inches) of the bob as a function of time t (in seconds) after release. Assume that a displacement of the right of the equilibrium position is positive. b) Find the position and direction of movement of the bob at t=1.25 sec.
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.
The bob on a simple pendulum is pulled to the left 4 in. from its equilibrium position. After release, the pendulum makes one complete back-and-forth cycle in 2 sec and follows
a) Write a function to model the displacement d (in inches) of the bob as a function of time t (in seconds) after release. Assume that a displacement of the right of the equilibrium position is positive.
b) Find the position and direction of movement of the bob at t=1.25 sec.
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