Answer to Question #218132 in Classical Mechanics for Help

Question

Use the following information to answer the next 2 questions:

A 25.0-kg child in Red Deer pumps herself on a swing when she kicks upward on the downswing, thus changing the distance from the pivot point to her centre of gravity from 2.40 m to 2.28 m.

1) The resonant frequency of her swing before the kick is: ___ Hz. 

2) The resonant frequency of her swing after the kick is: ___ Hz.

In the statements listed below, fill in the blanks with the best answer listed ont the bottom. Note that some answers may be used more than once!

3) Engineers build energy ________ systems into buildings so that an earthquake will not destroy them easily.

4) The periodic push that a child exerts on the swing must match the ________ frequency of the swing.

5) Compared to audible sound, the frequency of earthquake waves are generally very ________.

6) Every oscillating system has a ________ frequency, which is determined by the physical properties of the object.

1.forced

2.resonant

3.high

4.low

5.damping

Answer 1

1)

$$f_1=\frac{1}{2\pi}\sqrt{\frac{9.8}{2.4}}=0.322\ Hz$$

2)

$$f_2=\frac{1}{2\pi}\sqrt{\frac{9.8}{2.28}}=0.330\ Hz$$

3) Stabilization

4) Resonant

5) Lower

6) Resonant