A baby bounces up and down in her crib. Her mass is 11.0 kg, and the crib mattress can be modeled as a light spring with force constant 588 N/m. (a) The baby soon learns to bounce with maximum amplitude and minimum effort by bending her knees at what frequency? 3 Your response differs from the correct answer by more than 100%. Hz (b) If she were to use the mattress as a trampoline-losing contact with it for part of each cycle-what minimum amplitude of oscillation does she require?
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.
Since there are two more questions, each has two more subparts. we will answer the first question only.
The mass of the baby,
The crib mattress modelled as a light spring with force constant,
The relation between the frequency of oscillations of spring with the force constant and the mass of the object is,
Substitute,
Therefore, the frequency which baby bounces with maximum amplitude and minimum effort by bending her knees is 1.164 Hz.
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