7.4. Solution to the Equation of Motion

Try these first

1. 1.

   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.

2. 2.

   Define the term 'natural frequency'.

   Hint

   Consider how the system oscillates when disturbed.

3. 3.

   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.

4. 4.

   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.

5. 5.

   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.

6. 6.

   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.