An object of mass m can be hung from a rope (with linear mass density = 0.002 kg/m) that passes over a light pulley. The string is connected to a vibrator (which makes the string oscillate with a constant frequency f) and the length of the string between the point where the string is attached to the vibrator and the pulley is L = 2 m. When the mass of the object is m = 25 kg or m = 16 kg, standing waves are observed; however, no standing waves are observed with any other mass between these values, which means that they correspond to consecutive nodes, n and n + 1. a) What is the value of the tension of the string, FT, corresponding to each of the masses? b) In what harmonic does the string vibrate when the mass m = 25 kg is hung?
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.
An object of mass m can be hung from a rope (with linear mass density = 0.002 kg/m) that passes over a light pulley. The string is connected to a vibrator (which makes the string oscillate with a constant frequency f) and the length of the string between the point where the string is attached to the vibrator and the pulley is L = 2 m. When the mass of the object is m = 25 kg or m = 16 kg, standing waves are observed; however, no standing waves are observed with any other mass between these values, which means that they correspond to consecutive nodes, n and n + 1.
a) What is the value of the tension of the string, FT, corresponding to each of the masses?
b) In what harmonic does the string vibrate when the mass m = 25 kg is hung?
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