A 5.80 kg object on a horizontal frictionless surface is attached to a spring wi

Question

A 5.80 kg object on a horizontal frictionless surface is attached to a spring with spring constant 900 N/m. The object is displaced from equilibrium 50.0 cm horizontally (in the + direction) and given an initial velocity of 10.9 m/s back toward the equilibrium point at t=0 s.

(a) What is the frequency of the motion?
1.983 Hz

(b) What is the initial potential energy of the block-spring system?
112.5 J

(c) What is the initial kinetic energy?
344.5J

(d) What is the amplitude of the oscillation?
1.001m

(e) Write down the equation: Please fill in the numerical values for A, and below, in SI units. Use a positive value.
x(t) =1.001 · cos(12.457 · t + 1.0478 )

(f) What is the smallest possible NEGATIVE phase angle that could be used to describe this motion?
= ???? rad

Explanation / Answer

f)

x(t) =1.001 · cos(12.457 · t + 1.0478 )

This equation will hold true for all angle with increment of 2*pi

That is x(t) =1.001 · cos(12.457 · t + 1.0478 +2n*pi), where n is any integer

So for smallest phase angle we can take n = -1

=> x(t) =1.001 · cos(12.457 · t - 5.2353)

So the smallest possible NEGATIVE phase angle that could be used to describe this motion = - 5.2353 radians

[ I am assuming you need the answer for part f only as you have made it bold and put question mark on it. In case you need help with the other parts too please leave a message in the comment, I will update the solution then to include other parts. I am also assuming that the answer of part e is correct as that is needed to solve part f. ]

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