Cousin Throckmorton holds one end of the clothesline taut and wiggles it up and down sinusoidally. The average power that Throckmorton puts into the clothesline is small, about 1 WW. How much better can you do? Assume a rope that has linear mass density 0.500 kg/mkg/m, so 1 mm of the rope weighs about 1 lblb. The rope is long and is attached to a post at one end. You hold the other end of the rope in your hand and supply sinusoidal wave pulses by moving your arm up and down. Take the amplitude of the pulses to be 60 cmcm, the maximum tension you can supply to the rope by pulling on it horizontally to be 100 NN, and the time for you to complete each pulse to be 0.5 ss. Ignoring any effects from reflection of the pulses from the other end of the rope, what average power can you supply to the rope? Express your answer with the appropriate units.
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.
Cousin Throckmorton holds one end of the clothesline taut and wiggles it up and down sinusoidally. The average power that Throckmorton puts into the clothesline is small, about 1 WW. How much better can you do? Assume a rope that has linear mass density 0.500 kg/mkg/m, so 1 mm of the rope weighs about 1 lblb. The rope is long and is attached to a post at one end. You hold the other end of the rope in your hand and supply sinusoidal wave pulses by moving your arm up and down. Take the amplitude of the pulses to be 60 cmcm, the maximum tension you can supply to the rope by pulling on it horizontally to be 100 NN, and the time for you to complete each pulse to be 0.5 ss.
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