A 0.417 kg mass is attached to a string with a force constant of 53.9 N/m. The mass is displaced 0.286m from equilibrium and released. Assuming SHM for the system. Part A: With what frequency does it vibrate ? Part B: What is the speed of the mass when it is 0.143m from equilibrium? Part C: What is the total energy stored in this system?
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.
A 0.417 kg mass is attached to a string with a force constant of 53.9 N/m. The mass is displaced 0.286m from equilibrium and released. Assuming
Part A: With what frequency does it vibrate ?
Part B: What is the speed of the mass when it is 0.143m from equilibrium?
Part C: What is the total energy stored in this system?
Part D: What is the ratio of the kinetic energy to the potential energy when it is at 0.143m from equilibrium?
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Part D: What is the ratio of the kinetic energy to the potential energy when it is at 0.143m from equilibrium?
Part E: Draw a graph with kinetic energy, potential energy, and total mechanical energy as functions of time.
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