A 2.50 kg mass attached to spring constant of 25.0 N/m oscillates on a horizonta

Question

A 2.50 kg mass attached to spring constant of 25.0 N/m oscillates on a horizontal , frictionless track. At t= 0, the mass is released from rest at X= +10.0 cm (that is, the spring stretched by 10.0 cm). Determine the frequency of the oscillations, determine the maximum speed of the mass, determine the maximum acceleration of the mass, determine the total energy of the oscillating system, express the displacement as a function of time ( equation form) Thanks a lot A 2.50 kg mass attached to spring constant of 25.0 N/m oscillates on a horizontal , frictionless track. At t= 0, the mass is released from rest at X= +10.0 cm (that is, the spring stretched by 10.0 cm). Determine the frequency of the oscillations, determine the maximum speed of the mass, determine the maximum acceleration of the mass, determine the total energy of the oscillating system, express the displacement as a function of time ( equation form) Thanks a lot Thanks a lot

Explanation / Answer

a)
Period = 2pi sqrt(1.00 / 25.0)
= 1.26 sec.
freq=1/time period=1/1.26
(b)
Max. speed = 10.00 sqrt(5)
= 6.71 cm/sec.

Max. acceleration
= 10 * 3.00
= 30.00 cm/sec^2.

(c)
x = - 10.00 cos[ t sqrt(5) ] cm.
x' = 10.00 sqrt(5) sin[ t sqrt(5) ] cm/sec.
x'' = 50.00 cos[ t sqrt(5) ] cm/sec^2.

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