A jack-in-the-box undergoes simple harmonic motion after it pops out of its box with a frequency of 4.0 Hz and an amplitude of 19 cm. (a) What is the maximum acceleration experienced by the jack-in-the-box? m/s2 (b) If the mass of the jack-in-the-box is 0.180 kg, what is the maximum net force it experiences during the motion? N (c) If the initial phase angle is A?€/3 rad, write an equation that describes the net force as a function of time. (Assume SI base units and the angles are in radians. Do not include units in your answer. Use the following as necessary: t.) F(t) =
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 jack-in-the-box undergoes simple harmonic motion after it pops out of its box with a frequency of 4.0 Hz and an amplitude of 19 cm.
(a) What is the maximum acceleration experienced by the
jack-in-the-box?
m/s2
(b) If the mass of the jack-in-the-box is 0.180 kg, what is the
maximum net force it experiences during the motion?
N
(c) If the initial phase angle is A?€/3 rad, write an
equation that describes the net force as a function of time.
(Assume SI base units and the angles are in radians. Do not include
units in your answer. Use the following as necessary:
t.)
F(t) =
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