Question

1. Determine thedisplacement of a periodic motion given that the time it takes to complete one cycle is 1 second and the amplitude is 1 meter (y=-3.071790 x 10-⁷ m)

2. What is the angular frequency of an oscillating device at a period of 150 ms? (w=2400°/sec or 41.8879 rad/sec)

3. A pendulum is observed to complete 20 full cycles in 58 seconds. Determine the frequency (f = 0.34 cycle/sec)

4. Determine the frequencies of the following periods

a. 30 seconds

b. 3 seconds

c. 30 ms

d. 3000 seconds

Answer 1

1. The displacement in 1 s is

$$y=A\sin(\omega t)=A\sin\bigg(\frac{2\pi}Tt\bigg)=0.$$

2. We have

$$\omega=2\pi/T=41.89\text{ rad/s}.$$

3. The frequency is

$$f=\frac1T=\frac Nt=0.34\text{ Hz}.$$

4. The frequencies are

$$f_a=\frac 1{T_a}=0.033\text{ Hz},\\\space\\ f_b=\frac 1{T_b}=0.33\text{ Hz},\\\space\\ f_c=\frac 1{T_c}=33\text{ Hz},\\\space\\ f_d=\frac 1{T_d}=3.3·10^{-4}\text{ Hz}.$$