Calculate the mass of the block, the period of the motion, and the maximum speed of the block.   A block of unknown mass is attached to a spring with a spring constant of 10 N/m and undergoes...

Calculate the mass of the block, the period of the motion, and the maximum speed of the block.

 

A block of unknown mass is attached to a spring with a spring constant of 10 N/m and undergoes simple harmonic motion with an amplitude of 8.0 cm. When the block is 1/4 of the way between its equilibrium position and the endpoint, its speed is measured to be 30.0 cm/s.

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To calculate the block's mass, first calculate the energy of the system using the formula `E=1/2kA^2` , where E is the energy in Joules, k is the spring constant in N/m, and A is the amplitude in m. Converting 8 cm into meters gives 0.08 m for the amplitude. So

`E=1/2kA^2=1/2(10)(0.08^2)=0.032 J`

Since the total energy of the system is the sum of its kinetic and...

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