Answered: A mass m = 1.1 kg hangs at the end of a…

A mass m = 1.1 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

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Question

A mass m = 1.1 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 magnitude 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, φ, ω, and t.
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?

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

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