A 1.2-m string of mass 12 g is tied to the ceiling at its upper end, and the lower end supports a mass M. Neglect the very small variation in tension along the length of the string that is produced by the weight of the string. When you pluck the string slightly, the waves traveling up the string obey the equation y(x, t) = (2 mm)cos [(9.8 m-1)x - (490 s-1)t ] Assume that the tension of the string is constant and the gravitational acceleration = 9.8 m/s2. (a) What is the wavelength of the wave? (b) How much time does it take a pulse to travel the full length of the string? (c) Determine the value of the mass M?
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 1.2-m string of mass 12 g is tied to the ceiling at its upper end, and the lower end supports a mass M. Neglect the very small variation in tension along the length of the string that is produced by the weight of the string. When you pluck the string slightly, the waves traveling up the string obey the equation
y(x, t) = (2 mm)cos [(9.8 m-1)x - (490 s-1)t ]
Assume that the tension of the string is constant and the gravitational acceleration = 9.8 m/s2.
(a) What is the wavelength of the wave?
(b) How much time does it take a pulse to travel the full length of the string?
(c) Determine the value of the mass M?
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