A 0.25 kg mass attached to a spring oscillates along a horizontal frictionless s

Question

A 0.25 kg mass attached to a spring oscillates along a horizontal frictionless surface with amplitude A=7.5 cm and maximum speed vmax= 1.5 m/s.

a. Determine the spring constant

b. Determine the period of motion

c. Determine the maximum acceleration experienced by the mass

d. Determine the total energy of the system

A 0.25 kg mass attached to a spring oscillates along a horizontal frictionless surface with amplitude A=7.5 cm and maximum speed vmax= 1.5 m/s. a. Determine the spring constant b. Determine the period of motion c. Determine the maximum acceleration experienced by the mass d. Determine the total energy of the system

Explanation / Answer

1) Vmax = Aw
=> w = Vmax/A = 1.5/7.5 =1/5 = sqrt(k/m)
=> 0.25/25 =k
k =0.01 N/m
2) period =2pi/w = 10pi
3)Amax = Aw^2 = 7.5 * 1/5 *1/5 = 0.3 m/s^2
4) Total energy = 1/2 mv^2 = 0.125 *1.5^2 = 0.28125J

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