IC-3 A 167 gram mass is vibrating about its equilibrium position on the end of a spring as shown in problem SHM-8. While vibrating, the mass is observed to have a maximum speed of 0.500m/s and a maximum acceleration of 6.00m/s. At t-0 the mass is at the equilibrium position with a velocity to the left. a) Find the numerical values for the angular frequency o and the amplitude of the motion xm. Hint: think about how Vm and xm are related. b) Find the value of the spring constant of the spring. c) The position of the block is described by x-Xmcos(ot+0.). Find all possible values of 0, and then explain how to determine the value of 0, that corresponds to the given conditions.
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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