a) What is the frequency (in Hz) of the damped oscillation? b) By what percentage does the amplitude of the oscillation decrease in each cycle? c) Over what time interval (in s) does the energy of the system drop to 4.00% of its initial value?
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 metal block with a mass of 6.40 kg oscillates at the end of a vertical spring with a spring constant of 2.20 ✕ 104 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N · s/m
a) What is the frequency (in Hz) of the damped oscillation?
b) By what percentage does the amplitude of the oscillation decrease in each cycle?
c) Over what time interval (in s) does the energy of the system drop to 4.00% of its initial value?
d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b = 150 N · s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? What is the percentage decrease in amplitude in each cycle? What is the time interval (in s) for the energy to drop to 4.00% of its initial value?
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