A spring-mass system has a spring constant of k = 5 g/s². What mass should be attached to make the resulting motion have a frequency of 30 Hz? Assume that Hooke's law is applicable, resistance is negligible, and the mass of the spring is negligible. /
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.
![Problem 2 (Exercise 2.5.14)
A spring-mass system has a spring constant of k = 5 g/s?. What mass should be attached to make the resulting
motion have a frequency of 30 Hz? Assume that Hooke's law is applicable, resistance is negligible, and the mass
of the spring is negligible. /
Warning: Remember that w, is the circular/angular frequency. The actual frequency is computed from it as
Wo
frequency
27
which is on p. 83 in the filled-out lecture notes.
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