Q.2 (a) Using Newton's 2nd Law on the standard spring-mass model, show that the equation of motion of the damped harmonic oscillator of mass M, with damping constant B and spring stiffness k, is Eq.2 M 0.0 dx(t) dt + B dx (t) dt + kx(t) = 0 (b) Find the general solution of Eq.2 for M = 4, B = 2 and k = 3. (c) What is the solution of Eq.2 for th solutionspile.com

Question

Q.2 (a) Using Newton's 2nd Law on the standard spring-mass model, show that the equation of motion of the damped harmonic oscillator of mass M, with damping constant B and spring stiffness k, is Eq.2 M 0.0 d²x(t) dt² + B dx (t) dt + kx(t) = 0 (b) Find the general solution of Eq.2 for M = 4, B = 2 and k = 3. (c) What is the solution of Eq.2 for the special case k = 0, interpret this solution physically. (d) What is the solution of Eq.2 for the special case ß = 0, interpret this solution physically. (e) Using the expression for x(t) in part (b), find an expression for the velocity of the damped oscillator at t = 1. 1 M

student submitted image, transcription available below

(a) Using Newton's

2^{nd}

Law on the standard spring-mass model, show that the equation of motion of the damped harmonic oscillator of mass

M

, with damping constant

?

and spring stiffness

k

, is Eq.2

M \frac{d ^{2} x ( t )}{d t ^{2}} + ? \frac{d x ( t )}{d t} + k x (t) = 0

(b) Find the general solution of Eq.2 for

M = 4, ? = 2

and

k = 3

. (c) What is the solution of Eq.2 for the special case

k = 0

, interpret this solution physically. (d) What is the solution of Eq.2 for the special case

? = 0

, interpret this solution physically. (e) Using the expression for

x (t)

in part (b), find an expression for the velocity of the damped oscillator at

t = 1

.

Accepted Answer

Expert Answer to - Q.2 (a) Using Newton's 2nd Law on the standard spring-mass model, show that the equation of motion o

Answer

Solution for - Q.2 (a) Using Newton's 2nd Law on the standard spring-mass model, show that the equation of motion o

Answer

This an additional answer to - Q.2 (a) Using Newton's 2nd Law on the standard spring-mass model, show that the equation of motion o

(Solved): Q.2 (a) Using Newton's 2nd Law on the standard spring-mass model, show that the equation of motion o ...

View Expert Answer

Expert Answer

Buy This Answer $5

Place Order

We Provide Services Across The Globe