Practice Solution to the Equation of Motion - 7.4 | 7. Free Vibration of Single Degree of Freedom (SDOF) System | Earthquake Engineering - Vol 1
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Solution to the Equation of Motion

7.4 - Solution to the Equation of Motion

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the general form of the solution to the equation of motion for an SDOF system?

💡 Hint: Think about how sine and cosine functions are used together.

Question 2 Easy

Define the term 'natural frequency'.

💡 Hint: Consider how the system oscillates when disturbed.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the equation of motion for an undamped SDOF system?

mx¨(t) + kx(t) = 0
mx¨(t) + cx˙(t) + kx(t) = 0
kx(t) = 0

💡 Hint: Remember, damping would modify the equation.

Question 2

True or False: The phase angle ϕ can be derived from constants A and B.

True
False

💡 Hint: Recall how to qualify the angle from the ratio of constants.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

An SDOF system has a spring constant of 300 N/m and a mass of 15 kg. Calculate both its natural frequency and the amplitude if it starts from rest at a displacement of 0.5 m.

💡 Hint: Use the natural frequency formula and consider the initial conditions.

Challenge 2 Hard

Given the equation x(t) = 2cos(5t) + 3sin(5t), determine the amplitude and phase angle.

💡 Hint: Apply the formulas for amplitude and phase derived from A and B.

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