Chapter 11, Problem 75GP

a.

To determine

To find: The frequency of the pendulum towards upwards.

Answer to Problem 75GP

The frequency of the pendulum towards upwards is $1.22f$ .

Explanation of Solution

Given Information:

Frequency of pendulum = $f$

Acceleration of pendulum = $0.5g$

Concept used:

The frequency of the oscillation of the pendulum is

  $f=2\pi \sqrt{\frac{g}{l}}$

Where, g is the acceleration and l is the length of the pendulum.

Calculation:

  $f=2\pi \sqrt{\frac{g}{l}}$

  $\begin{array}{l}{f}_u=2\pi \sqrt{\frac{g+0.5g}{l}}\\ f_u=f\sqrt{1+0.5}\\ f_u=f\sqrt{1.5}\\ f_u=1.22f\end{array}$

Conclusion:

The upward frequency of the pendulum is $1.22f$ .

To determine

To Find: The downward frequency of the pendulum.

Answer to Problem 75GP

The downward frequency of the pendulum is $0.71f$ .

Explanation of Solution

Given Information:

Frequency of pendulum = $f$

Acceleration of pendulum = $0.5g$

Concept used:

The frequency of the oscillation of the pendulum is

  $f=2\pi \sqrt{\frac{g}{l}}$

Calculation:

As, $f=2\pi \sqrt{\frac{g}{l}}$

  $\begin{array}{l}{f}_d=2\pi \sqrt{\frac{g-0.5g}{l}}\\ f_d=f\sqrt{1-0.5}\\ f_d=f\sqrt{0.5}\\ f_d=0.71f\end{array}$

Conclusion:

The downward frequency of the pendulum is $0.71f$ .