3. In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x = 5.00 cos (2t +) where x is in centimeters and t is in seconds. At t = 0, find the following: a. the position of the particle, x, b. its velocity, v, Hint: Differentiate the given equation for x OR use the equation of v from the discussion above, first then substitute t = 0. c. its acceleration, a, Hint: Differentiate the obtained equation for v OR use the equation of q from the discussion above, first then substitute t = 0. d. the period, T, and e. the amplitude, A of the motion. Hint: No need to compute, just compare the equation of the displacement for SHM and the given equation in this problem, then identify the value of A.
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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