Question

Figure 1. A one-dimensional spring-mass-damper system. Given variables: m - mass k - spring constant b - damping constant x - distance travelled F - force applied at the center of mass in the direction of positive x The differential equation of the mass-spring-damper system is m d^2x/dt^2 + b dx/dt + kx = F Assume that m = 1kg, b = 0.1, k = 0.2, and F = 3 sin(3t) Assume moreover that x(0) = 0 and dx/dt(0) = 1 meter per second. Compute the response of the mass-spring-damper system from time t = 0 to time t = 10 s. Plot x and dx/dt as functions of time. A What does the plot look like? [Hint: The response can be solved in several ways. One way is to use ode45 in matlab. Type "help ode45" in the command window to see how to use it.] B What is the value of x at t = 10s? [Precision: 1 decimal place] C What is the value of dx/dt at t = 5s? [Precision: 1 decimal place]

          Figure 1. A one-dimensional spring-mass-damper system.

Given variables:
m - mass
k - spring constant
b - damping constant
x - distance travelled
F - force applied at the center of mass in the direction of positive x

The differential equation of the mass-spring-damper system is
m d^2x/dt^2 + b dx/dt + kx = F

Assume that m = 1kg, b = 0.1, k = 0.2, and F = 3 sin(3t)
Assume moreover that x(0) = 0 and dx/dt(0) = 1 meter per second.

Compute the response of the mass-spring-damper system from time t = 0 to time t = 10 s. Plot x and dx/dt as functions of time.

A What does the plot look like?
[Hint: The response can be solved in several ways. One way is to use ode45 in matlab.
Type "help ode45" in the command window to see how to use it.]

B What is the value of x at t = 10s?
[Precision: 1 decimal place]

C What is the value of dx/dt at t = 5s?
[Precision: 1 decimal place]

Figure 1. A one-dimensional spring-mass-damper system.

Given variables:
m - mass
k - spring constant
b - damping constant
x - distance travelled
F - force applied at the center of mass in the direction of positive x

The differential equation of the mass-spring-damper system is
m d^2x/dt^2 + b dx/dt + kx = F

Assume that m = 1kg, b = 0.1, k = 0.2, and F = 3 sin(3t)
Assume moreover that x(0) = 0 and dx/dt(0) = 1 meter per second.

Compute the response of the mass-spring-damper system from time t = 0 to time t = 10 s. Plot x and dx/dt as functions of time.

A What does the plot look like?
[Hint: The response can be solved in several ways. One way is to use ode45 in matlab.
Type "help ode45" in the command window to see how to use it.]

B What is the value of x at t = 10s?
[Precision: 1 decimal place]

C What is the value of dx/dt at t = 5s?
[Precision: 1 decimal place]

Added by Tina D.

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