Problem 2: We have two different vertical mass-spring systems, as shown in the figure below. (a). What is the frequency of system A? What is the first time at which the mass has maximum speed while traveling in the upward direction? (b). What is the period of system B? What is the first time at which the energy is entirely potential? (c). Given that the mass is the same in both systems, what is the ratio of their spring constants? That is what is kA/kB? y B KOAL -t (s)
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.
We have two different vertical mass-spring systems, as shown in the figure below.
(a). What is the frequency of system A? What is the first time at which the mass has maximum speed while
traveling in the upward direction?
(b). What is the period of system B? What is the first time at which the energy is entirely potential?
(c). Given that the mass is the same in both systems, what is the ratio of their spring constants? That is
what is kA/kB?
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