Chapter 6.4, Problem 61E

(a)

To determine

To Find: The period and frequency of the spring if the first weight has the mass $0.4kg$ .

Answer to Problem 61E

  $0.9s/cycle,1.1hertz$

Explanation of Solution

Given:Equation $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$ .

Given: $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$

Substitute $m=0.4$

  $\begin{array}{l}y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)\\ y=1.5\cos \left(t\sqrt{\frac{18.5}{0.4}}\right)\\ y=1.5\cos 6.8t\\ \frac{2\pi }{k}=6.8\\ k=0.9s/cycle\\ f=\frac{1}{k}=\frac{1}{0.9}=1.1hertz\end{array}$

(b)

To determine

To Find: The period and frequency of the spring if the second weight has the mass $0.6kg$ .

Answer to Problem 61E

  $1.1s/cycle,0.9hertz$

Explanation of Solution

Given: Equation $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$ .

Given: $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$

Substitute $m=0.6$

  $\begin{array}{l}y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)\\ y=1.5\cos \left(t\sqrt{\frac{18.5}{0.6}}\right)\\ y=1.5\cos 5.6t\\ \frac{2\pi }{k}=5.6\\ k=1.1s/cycle\\ f=\frac{1}{k}=\frac{1}{1.1}=0.9hertz\end{array}$

(c)

To determine

To Find: The period and frequency of the spring if the third weight has the mass $0.8kg$ .

Answer to Problem 61E

  $1.3s/cycle,0.8hertz$

Explanation of Solution

Given: Equation $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$ .

Given: $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$

Substitute $m=0.8$

  $\begin{array}{l}y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)\\ y=1.5\cos \left(t\sqrt{\frac{18.5}{0.8}}\right)\\ y=1.5\cos 4.8t\\ \frac{2\pi }{k}=4.8\\ k=1.3s/cycle\\ f=\frac{1}{k}=\frac{1}{1.3}=0.8hertz\end{array}$

(d)

To determine

To Find: As the mass increases what happen to the period.

Answer to Problem 61E

Increases.

Explanation of Solution

Given: Equation $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$ .

Given: $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$

The period increases as the mass increases.

(e)

To determine

To Find: As the mass increases what happen to the frequency.

Answer to Problem 61E

Decreases.

Explanation of Solution

Given: Equation $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$ .

Given: $y=1.5\cos \left(t\sqrt{\frac{k}{m}}\right)$

The frequency deccreases as the mass increases.