A mass connected to a spring undergoes simple harmonic motion on a friction less

Question

A mass connected to a spring undergoes simple harmonic motion on a friction less surface. The following observations are made. The position of the mass at t = 1 s is x = (1 m)i from its equilibrium position, the velocity of the mass at t = 1 s is v = (2 m/s)i. and the acceleration at t = 1 s is a = (-3 m/s^2)i. Your answers should l)C numerical with proper units and can be in terms of square roots, trigonometric functions and/or their inverses. Determine the angular frequency (u) of the mass's motion, Determine the phase angle (Phi) of the mass's motion. Determine the amplitude A of the mass's motion.

Explanation / Answer

A ) Acceleration A = w^2 × displacement

Angular velocity w = sqrt A/ x = ~/ 3 ÷ 1

= sqrt 3 rad/ s = 1.732 rad/s

C ) for amplitude a

velocity v^2 = w^2 (a^2 -x^2 )

2^2 =( ~/3)^2 ( a^2-1^2 )

a= sqrt 7/3 = 1.5275 m

B ) phase angle ( phi ) is the displacement at time t = 0

x = a sin ( wt + phi)

1 = 1.5275 sin ( ~/ 3 × 1 + phi)

Phi = sin^-1 (0.6555 )- 1.732 rad

= -1.06 rad

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