7.4 - Solution to the Equation of Motion
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Practice Questions
Test your understanding with targeted questions
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.
Define the term 'natural frequency'.
💡 Hint: Consider how the system oscillates when disturbed.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the equation of motion for an undamped SDOF system?
💡 Hint: Remember, damping would modify the equation.
True or False: The phase angle ϕ can be derived from constants A and B.
💡 Hint: Recall how to qualify the angle from the ratio of constants.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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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