Question

A 1.30 kg mass on a spring oscillates horizontally with little friction according to the following equation: x=0.0500cos(2.90t) where x is in m and t in s. Find the maximum energy stored in the spring during an oscillation.

Answer 1

The maximum energy stored in the spring during an oscillation is 0.00612 J.

Step-by-step explanation:

To find the maximum energy stored in the spring during an oscillation, we can use the equation for potential energy of a spring, which is U = (1/2)kA², where U is the potential energy, k is the force constant of the spring, and A is the amplitude. In this case, the force constant k is given as 4.90 N/m. To find A, we can use the equation given, which is x = 0.0500cos(2.90t). The maximum amplitude can be found by taking the maximum value of the cosine function, which is 1. Therefore, A = 0.0500 m. Plugging in the values into the equation for potential energy, we get U = (1/2)(4.90 N/m)(0.0500 m)² = 0.00612 J.