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# A 1 kg mass is on a horizontal frictionless surface and is attached to a horizontal...

A 1 kg mass is on a horizontal frictionless surface and is attached to a horizontal spring with a spring constant of 144 N/m. The spring's unstretched length is 20 cm. You pull on the mass and stretch the spring 5 cm and release it. The period of its oscillations is T=.524s The amplitude of the block's oscillatory motion is 5cm The maximum velocity of the oscillating mass is 60cm/s Part E) While the frictionless surface is working well, the mass itself is not extremely aerodynamic and some drag force is inevitable. The drag force is proportional to the velocity of the block as described in Chapter 15. After 18 cycles you observe that the maximum displacement has decreased from 5 cm to 4.5 cm. What is the value of the damping constant? (Enter your answer with 4 significant figures) Part F)What is the position of the mass at 15 seconds? What is magnitude of its velocity at that instant? Part G)The mass spring system is now flipped vertically such that gravity must be included in the formulation of our governing equations. When the mass is resting (stationary) on the spring, how much is the spring compressed relative to its equilibrium position? Part H) While the mass is resting at its equilibrium position on the spring, you hit the mass downward with a hammer. The average force of your hammer strike is 200 N and its duration is 1 ms. What is the period of the oscillations after the hammer strike? Part I)After you strike the mass with a hammer, the impulse creates a nearly instantaneous velocity. What is the velocity of the block immediately after the hammer strike? Part J)You begin tracking the vertical position of the mass, y(t), immediately after the hammer strike. Recall that at t = 0, the mass is sitting at the new equilibrium positon determined by the balance of spring force and gravitational force. We call this new equilibrium position y = 0 and the mass will oscillate around this zero point with y(t) positive when above equilibrium and y(t) negative when below equilibrium. To correctly describe the motion of the mass, what is the necessary phase constant? Part K) What is the maximum amplitude of oscillation of the mass after the hammer strike?

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