A 10-kg mass is attached to a spring having a spring constant of 140 N/m. The mass is started in motion from the equilibrium position with an initial velocity of 1 m/sec in the upward direc-tion and with an applied external force given by ƒ(t) = 5 sin t (in newtons). The mass is in a viscous medium with a coefficient of resistance equal to 90 N-sec/m. Formulate an initial value prob-lem that models the given system; solve the model and interpret the results.

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A: Solution is attached below:

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A: Step 1:

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A: Solution is given below.

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A:

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A:

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A:

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A:

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A: In this problem, it is asking for which type of spring has larger spring constant.

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A:

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A:

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A: Weight attached (m)= 20 kg Spring constant (k)= 320 kg/m F(t)= 1200cos(2t)

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A: Givenm=1.35kgk=440 N/mθ=22o∆x=3cm=0.03m

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.