Free Printable SDOF Review 1

1.

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

a)

$\sqrt{\frac{B}{A}}$

b)

$\sqrt{\frac{A}{B}}$

c)

$\sqrt{AB}$

d)

No vibrations

2.

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?

a)

$C$

b)

$\sqrt{\left(C\right)}$

c)

$-C$

d)

No oscillations

3.

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

a)

$\sqrt{\frac{k}{m}+g}$

b)

$\sqrt{\frac{k\cos^2\theta}{m}}$

c)

$\sqrt{\frac{k}{m}}$

d)

$\sqrt{\frac{k\cos\theta}{m}^{ }}$

4.

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

a)

$mg$

b)

$\frac{mg}{k}$

c)

$\frac{k}{mg}$

d)

Insufficient information

5.

Initial conditions directly impact the natural frequency of the system

a)

True

b)

False

6.

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:

a)

Double the natural frequency

b)

Double the period of oscillations

c)

Halve the period of oscillations

d)

None of the above

7.

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

a)

1 Hz

b)

0.01 Hz

c)

1 rad/s

d)

0.01 rad/s

SDOF Review 1

Total questions: 7

Worksheet time: 4mins

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