Calculating Speed of Simple Harmonic Motion with Initial Displacement

AI Thread Summary
To calculate the speed of a 0.1 kg block in simple harmonic motion after being displaced 4 cm from equilibrium, the spring constant is 32 N/m and a frictional force of 0.3 N is present. The potential energy stored in the spring when displaced can be calculated using the formula for spring potential energy. As the block moves to the equilibrium position, this potential energy converts to kinetic energy while overcoming friction. The final speed can be determined by applying energy conservation principles, accounting for the work done against friction. The discussion emphasizes the importance of detailing initial calculations to facilitate assistance.
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Please help with the following problem:

A 0.1 kg block rests on a level surface and is attached to a horizontally aligned spring with a spring constant of 32 N/m. The block is initially displaced 4 cm from the equilibrium position and then released to set up a simple harmonic motion. A frictional force of 0.3 N exists between the block and the surface. What is the speed of the block when it passes through the equilibrium position after being released from the initial 4 cm displacement point?
 
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