You bounce on a huge trampoline and start oscillating up and down with a period of 3 s. After a long while, you come to rest but the trampoline below you is displaced below its natural height. How much is the trampoline bent in m? Model the trampoline as a spring.

Since the period is 3, the final displacement is 4.23

Wrong answer

To find out how much the trampoline is bent, we need to analyze the relationship between period and displacement for a spring-mass system. By Hooke's Law, the force exerted by a spring is directly proportional to its displacement from its equilibrium position.

The equation for the period of oscillation of a mass-spring system is given by:

T = 2π√(m/k)

Where:
T is the period of oscillation
m is the mass attached to the spring
k is the spring constant

In this case, the mass attached to the spring is your body, and T is given as 3 seconds. However, we do not know the value of k, which represents the spring constant.

To find the displacement (how much the trampoline is bent), we need to first find the spring constant, given the period.

Rearranging the formula for the period, we have:

k = (4π²m) / T²

Substituting the values we know:

k = (4π² * m) / (3²)

Now, the actual displacement of the trampoline below its natural height will depend on the mass of your body and the spring constant. Without the mass value or a way to estimate it, we cannot determine the exact displacement. However, we can conclude that the displacement will be greater for a larger mass and a smaller spring constant.

In summary, to find the exact displacement of the trampoline, we would need to know the mass of your body and the spring constant.