Question

A mass of 2kg stretches a spring 20cm. Suppose the mass is displaced an additional 12cm in the positive (downward) direction and then released. Suppose that the damping constant is 1 N · s/m and assume g = 9.8 m/s² is the gravitational acceleration. (a) Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, x', x''. (b) Enter the initial conditions: x(0) = m, x'(0) = m/s (c) Is this system under damped, over damped, or critically damped?

          A mass of 2kg stretches a spring 20cm. Suppose the mass is displaced an additional 12cm in the positive (downward) direction and then released. Suppose that the damping constant is 1 N · s/m and assume g = 9.8 m/s² is the gravitational acceleration.

(a) Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, x', x''.

(b) Enter the initial conditions:
x(0) = m,
x'(0) = m/s

(c) Is this system under damped, over damped, or critically damped?

Show more…

A mass of 2kg stretches a spring 20cm. Suppose the mass is displaced an additional 12cm in the positive (downward) direction and then released. Suppose that the damping constant is 1 N · s/m and assume g = 9.8 m/s² is the gravitational acceleration.

(a) Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, x', x”.

(b) Enter the initial conditions:
x(0) = m,
x'(0) = m/s

(c) Is this system under damped, over damped, or critically damped?

Added by Brett E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/22/2023

Step 1

First, we need to find the spring constant k. We know that the mass of 2 kg stretches the spring by 20 cm (0.2 m). Using Hooke's Law, F = kx, where F is the force exerted by the spring and x is the displacement from the equilibrium position. Show more…

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A mass of 2kg stretches a spring 20cm. Suppose the mass is displaced an additional 12cm in the positive (downward) direction and then released: Suppose that the damping constant is 1 N s/m and assume g == 9.8 m/s? is the gravitational acceleration: (a) Set up a differential equation that describes this system: Let to denote the displacement; in meters, of the mass from its equilibrium position, and give your answer in terms of , x (b) Enter the initial conditions: t(0) m (0) m over damped critically damped under damped (c) Is this system under damped_ over damped, or critically damped?

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