Question

A small block is attached to an ideal spring and is moving in shm on a horizontal, frictionless surface. when the amplitude of the motion is 0.090 m , it takes the block 2.86 s to travel from x = 0.090 m to x = -0.090 m .

Answer 1

The equation of motion for the block in simple harmonic motion attached to an ideal spring is x=A*cos(2πt/T), where A is the amplitude, t is the time, and T is the period of the motion. The equation for this specific case is x = 0.090 * cos(2πt/1.43).

Step-by-step explanation:

When a block attached to an ideal spring moves in simple harmonic motion (SHM), its position can be described by the equation x = A * cos(2πt/T), where x is the displacement from equilibrium, A is the amplitude of the motion, t is the time, and T is the period of the motion.

In this case, the amplitude is given as 0.090 m. We can determine the period of the motion by dividing the time it takes for the block to travel from x = 0.090 m to x = -0.090 m (2.86 s) by the number of complete oscillations in that time (2). Therefore, the period is 2.86 s / 2 = 1.43 s.

Substituting the values in the equation, we get x = 0.090 * cos(2πt/1.43) as the equation of motion for the block.