Question

Where x is in meters (m) and t is in seconds (s), find the maximum energy stored in the spring during an oscillation.

Answer 1

The maximum energy stored in the spring during an oscillation can be found using the equation for elastic potential energy. To find the maximum energy, we need to determine the maximum value of x, which can be found using the equation x(t) = √(2E/k)cos[(√k/m)t]. Once we have the maximum value of x, we can substitute it into the elastic potential energy equation and solve for U.

Step-by-step explanation:

The maximum energy stored in the spring during an oscillation can be found using the equation for elastic potential energy. The equation is U = 1/2kx², where U is the potential energy stored in the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position. To find the maximum energy, we need to determine the maximum value of x.

1. The maximum value of x can be found when the block reaches its maximum displacement, which is equal to the amplitude of the oscillation.
2. The value of x can be determined using the equation x(t) = √(2E/k)cos[(√k/m)t].
3. By substituting t = T/2 (where T is the period of the oscillation) into the equation, we can find the maximum value of x.

Once we have the maximum value of x, we can substitute it into the elastic potential energy equation and solve for U, giving us the maximum energy stored in the spring during an oscillation.