Holooly Plus Logo
Holooly Plus Logo

Question 2.9.3: Ramp Response with the lsim Function Plot the forced respons...

Ramp Response with the lsim Function

Plot the forced response of

ẍ + 3ẋ + 5x = 10f(t)

to a ramp input, u(t) = 1.5t, over the time interval 0 ≤ t ≤ 2.

This Question has been Answered.
Subscribe
Already have an account?
Login

Related Answered Questions

Question: 2.1.6

Find the complete response of the following equation. ẍ + 4ẋ + 53x = 15us(t) x(0) = 8 ẋ (0) = −19 ...

Verified Answer:

We cannot use Table 2.1.1 for this part because th...
Question: 2.9.2

Impulse Response of Second-Order Models In Example 2.6.4 we obtained the response of the following model to a unit impulse: X(s)/ F(s) = 1 / 2s² + 14s + 20 Our analysis showed that if x(0−) = ẋ(0−) = 0, then x(0+) = 0 and ẋ(0+) = 1∕2. Use the impulse function to verify these results. ...

Verified Answer:

Question: 2.9.1

Step Response of a Second-Order Model Consider the following model: X(s)/ F(s) = cs + 5 /10s² + cs + 5 a. Plot the unit-step response for c = 3 using the time span selected by MATLAB. b. Plot the unit-step response for c = 3 over the range 0 ≤ t ≤ 15. c. Plot the unit-step responses for c = 3 and ...

Verified Answer:

Question: 2.3.3

The Sine and Cosine Functions Derive the Laplace transforms of the exponentially decaying sine and cosine functions, e ^−at sin𝜔t and e ^−at cos𝜔t, for t ≥ 0, where a and 𝜔 are constants. ...

Verified Answer:

Note that from the Euler identity, e^{j\the...
Question: 2.7.7

Two Complex Roots Use two methods to obtain the inverse Laplace transform of X(s) = 3s + 7/4s² + 24s + 136 = 3s + 7/4(s² + 6s + 34) ...

Verified Answer:

a. The denominator roots are s = −3 ± 5j. To avoid...
Question: 2.7.5

Four Repeated Roots Choose the most convenient method for obtaining the inverse transform of X(s) = s² + 2/s^4(s + 1) ...

Verified Answer:

There are four repeated roots (s = 0) and one dist...
Question: 2.7.4

Exponential Response of a First-Order Model Use the Laplace transform to solve the following problem. ẋ + 5x = 7te ^−3t x(0) = 0 ...

Verified Answer:

Taking the transform of both sides of the equation...
Question: 2.7.2

One Negative Root and Two Zero Roots The inverse Laplace transform of X(s) = 5/s²(3s + 12) ...

Verified Answer:

The denominator roots are s= −12/3= −4, s=0, and s...
Question: 2.7.1

A Third-Order Equation Obtain the solution of the following problem: 10 d³x /dt³ + 100 d²x /dt² + 310 dx /dt + 300x = 750us(t) x(0) = 2 ẋ(0) = 4 ẍ(0) = 3 ...

Verified Answer:

Using the Laplace transform method, we have [latex...
Question: 2.6.6

Impulse Response of a Second-Order Model Obtain the unit-impulse response of the following model. The initial conditions are x(0−)=0, x ̇(0−) = 0. What are the values of x(0+) and x ̇(0+)? X(s) / F(s) = 1 / 2s²+ 14s + 20 ...

Verified Answer:

Because f(t) = 𝛿(t), F(s) = 1, and X(s)=\fr...