Answer to Question #182163 in Mechanical Engineering for luke

Question #182163

A spring has a stiffness of 100N/m. A mass of 4 kg was attached to the spring. The mass was pushed 10cm upward from the equilibrium position and was released from rest. After 5 seconds from release, determine the acceleration of the mass in m/s^2 *


1
Expert's answer
2021-04-21T07:05:59-0400

Since Mass was displaced by 10 cm from the mean position, its amplitude of vibration A=0.1 m

Since the body starts From an extreme position,

The displacement of mass after time t is given by

"X=A\\times cos(\\sqrt{\\frac{k}{m}}\\times t)"

The acceleration of mass after time t is given as

"a=- \\frac{k}{m}X=-\\frac{k}{m}\\times A\\times cos(\\sqrt{\\frac{k}{m}}\\times t)"

"a=-\\frac{100}{4}\\times 0.1\\times cos(\\sqrt{\\frac{100}{4}}\\times 5)=-2.478\\:m\/s^2"

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