Question

A block with mass m is undergoing shm on a horizontal, frictionless surface while attached to a light, horizontal spring that has force constant k . you use motion sensor equipment to measure the maximum speed of the block during its oscillations. you repeat the measurement for the same spring and blocks of different masses while keeping the amplitude a at a constant value of 14.0 cm . you plot your data as v2max versus 1/m and find that the data lie close to a straight line that has slope 9.62 n⋅m .

Answer 1

The maximum speed squared in simple harmonic motion is related to the inverse of the mass and has a direct proportionality with the spring constant and the square of the amplitude of oscillation. For a constant amplitude, the slope of the line in a plot of maximum speed squared against the inverse of mass corresponds to kA2.

Step-by-step explanation:

Understanding Simple Harmonic Motion (SHM) with Varying Masses

When discussing a block undergoing SHM on a frictionless surface connected to a spring with force constant k, the motion of the block can be described by simple harmonic motion equations. According to these, the maximum speed vmax of the block is when it passes through the equilibrium position (x=0).

The relationship between the maximum speed squared (vmax^2) and the mass of the block is given by vmax^2 = (k/m)A^2, where A is the amplitude of oscillation. When plotted as vmax^2 versus 1/m, the slope of the line should be kA2 according to this relationship. For a spring with amplitude kept at 14.0 cm, if the slope of the line in the given data is 9.62 N·m, this would correspond to the product of the spring constant k and amplitude squared A2 in the equation for maximum speed squared of the SHM.