A scene in a movie has a stuntman falling through a floor onto a bed in the room below. The plan is to have the actor fall on his back, but a researcher has been hired to investigate the safety of this stunt. When the researcher examines the mattress, she sees that it effectively has a spring constant of 77144N/mfor the area likely to be impacted by the stuntman, but it cannot depress more than 13.33cmwithout injuring him.To approach this problem, consider a simplified version of the situation. A mass falls through a height of 3.92mbefore landing on a spring of force constant 77144N/m. Calculate the maximum mass that can fall on the mattress without exceeding the maximum compression distance.
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 scene in a movie has a stuntman falling through a floor onto a bed in the room below. The plan is to have the actor fall on his back, but a researcher has been hired to investigate the safety of this stunt. When the researcher examines the mattress, she sees that it effectively has a spring constant of 77144N/mfor the area likely to be impacted by the stuntman, but it cannot depress more than 13.33cmwithout injuring him.To approach this problem, consider a simplified version of the situation. A mass falls through a height of 3.92mbefore landing on a spring of force constant 77144N/m. Calculate the maximum mass that can fall on the mattress without exceeding the maximum compression distance.
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