The device pictured in the figure entertains infants while keeping them from wandering. The child bounces in a harness, with a spring constant k, and is suspended off of the ground. a) If the spring stretches x1 = 0.225 m from equilibrium while supporting an 7.3-kg child, what is its spring constant, in newtons per meter? b) What is the time, in seconds, for one complete bounce of this child about the point x1? c) What is the child’s maximum velocity, in meters per second, if the amplitude of her bounce, relative to x1, is 0.195 m?
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.
The device pictured in the figure entertains infants while keeping them from wandering. The child bounces in a harness, with a spring constant k, and is suspended off of the ground.
a) If the spring stretches x1 = 0.225 m from equilibrium while supporting an 7.3-kg child, what is its spring constant, in newtons per meter?
b) What is the time, in seconds, for one complete bounce of this child about the point x1?
c) What is the child’s maximum velocity, in meters per second, if the amplitude of her bounce, relative to x1, is 0.195 m?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
