A common device for entertaininga toddler is a jump seat thathangs from the horizontal portion of adoorframe via elastic cords .Assume that only one cord is on eachside in spite of the more realisticarrangement shown.When a child isplaced in the seat, they both descend by a distance ds as the cordsstretch (treat them as springs).Then the seat is pulled down an extradistance dm and released, so that the child oscillates vertically,like a block on the end of a spring. Suppose you are the safety engineerfor the manufacturer of the seat.You do not want the magnitudeof the child’s acceleration to exceed 0.20g for fear of hurtingthe child’s neck. If dm =10 cm, what value of ds corresponds to thatacceleration magnitude?
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 common device for entertaining
a toddler is a jump seat that
hangs from the horizontal portion of a
doorframe via elastic cords .
Assume that only one cord is on each
side in spite of the more realistic
arrangement shown.When a child is
placed in the seat, they both descend by a distance ds as the cords
stretch (treat them as springs).Then the seat is pulled down an extra
distance dm and released, so that the child oscillates vertically,
like a block on the end of a spring. Suppose you are the safety engineer
for the manufacturer of the seat.You do not want the magnitude
of the child’s acceleration to exceed 0.20g for fear of hurting
the child’s neck. If dm =10 cm, what value of ds corresponds to that
acceleration magnitude?
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