Question

A mass m = 1.4 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k = 75 N/m and negligible mass. At time t = 0 the mass is released from rest at a distance d = 0.35 m below its equilibrium height and undergoes simple harmonic motion with its position given as a function of time by y(t) = A cos(ωt – φ). The positive y-axis points upward.

A) Find the angular frequency of oscillation, in radians per second.

B) Determine the value of the coefficient A, in meters.

C) Determine the value of φ, in radians.

D) Enter an expression for the velocity along the y-axis as a function of time, in terms of A, ω, and t, using the value for φ from the previous part.

E) What is the mass’s velocity, in meters per second, at time t1 = 0.25 s?

F) What is the magnitude of the mass’s maximum acceleration, in meters per second squared?

Please show all work

Answer 1