SDOF Review 1

What is the natural frequency of the system with an equation of motion  $A\frac{\text{d}^2x}{\text{d}t^2}+Bx\ =\ 0$ ?

•  $\sqrt{\frac{B}{A}}$  

•  $\sqrt{\frac{A}{B}}$  

•  $\sqrt{AB}$  

• No vibrations

 The equation $\frac{\text{d}^2x}{\text{d}t^2}-C^{ }x=0$ describes the behaviour of a system, where $C$  is a positive constant. What is the natural frequency of oscillation?

•  $C$  

•  $\sqrt{\left(C\right)}$  

•  $-C$  

• No oscillations

What is the natural frequency of this system? (Example 2-4)

• $\sqrt{\frac{k}{m}+g}$

• $\sqrt{\frac{k\cos^2\theta}{m}}$

• $\sqrt{\frac{k}{m}}$

• $\sqrt{\frac{k\cos\theta}{m}^{ }}$

The mass $m$ shown is attached to a spring of stiffness $k$ . At static equilibrium (no motion), what is the displacement of the spring?

•  $mg$  

•  $\frac{mg}{k}$  

•  $\frac{k}{mg}$  

• Insufficient information 

 Initial conditions directly impact the natural frequency of the system

• True

• False

 Assume a simple SDOF system where the E.O.M. is given by  $m\frac{\text{d}^{2\ }x}{\text{d}t^2}+kx=0$ Increasing the mass to  $4m$  would:

• Double the natural frequency

• Double the period of oscillations

• Halve the period of oscillations

• None of the above

A simple spring-mass system is undergoing vibrations. If the spring constant is  $k=1\$ N/m and the mass is  $m=1$  kg, then the natural frequency  $p=\sqrt{\frac{k}{m}}$  is calculated as

• 1 Hz

• 0.01 Hz

• 1 rad/s

• 0.01 rad/s