A spring with a k = 15 N/m, and a mass of m = 30g is pulled to x = +6m, and then given an initial velocity of v = +6 cm/s. a) What is the equation of motion ( x(t) = ? ) and plot the answer b) Plot the phase diagram of v vs x c) Now, the system is critically damped by friction. What is the value of b to achieve this? Solve for x(t) again, and sketch the answer d) At what location is the critically damped oscillator, when the undamped oscillater reaches x = 0 (equillibrium) initially? e) Plot this new phase diagram of v vs x of the critically damped mass, and compare/contrast with the undamped scenario.

A spring with a k = 15 N/m, and a mass of m = 30g is pulled to x = +6m, and then given an initial velocity of v = +6 cm/s. a) What is the equation of motion ( x(t) = ? ) and plot the answer b) Plot the phase diagram of v vs x c) Now, the system is critically damped by friction. What is the value of b to achieve this? Solve for x(t) again, and sketch the answer d) At what location is the critically damped oscillator, when the undamped oscillater reaches x = 0 (equillibrium) initially? e) Plot this new phase diagram of v vs x of the critically damped mass, and compare/contrast with the undamped scenario.

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Question

A spring with a k = 15 N/m, and a mass of m = 30g is pulled to x = +6m, and then given an initial velocity of v = +6 cm/s.

a) What is the equation of motion ( x(t) = ? ) and plot the answer
b) Plot the phase diagram of v vs x
c) Now, the system is critically damped by friction. What is the value of b to achieve this? Solve for x(t) again, and sketch the answer
d) At what location is the critically damped oscillator, when the undamped oscillater reaches x = 0 (equillibrium) initially?
e) Plot this new phase diagram of v vs x of the critically damped mass, and compare/contrast with the undamped scenario.

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