Question

two collinear shms, with amplitudes 5cm and 12cm are superposed, calculate the resultant amplitude when shm differ in phase by 60degree

Answer 1

Question.

two collinear shms, with amplitudes 5 cm and 12 cm are superposed, calculate the resultant amplitude when shm differ in phase by 60 degree

Solution

Equations of harmonic oscillations have the form:

$$x _ {1} = X _ {1} \cdot \cos \omega t \text{ and } x _ {2} = X _ {2} \cdot \cos (\omega t + \varphi_ {0}), X _ {1} = 12 \mathrm{cm}, X _ {2} = 5 \mathrm{cm}, \varphi_ {0} = \pi / 3.$$

As we can see from the vector diagram above, the resultant amplitude can be found as

$$X ^ {2} = X _ {1} ^ {2} + X _ {2} ^ {2} + 2 \cdot X _ {1} \cdot X _ {2} \cos \varphi_ {0} = 12 ^ {2} + 5 ^ {2} + 2 \cdot 12 \cdot 5 \cdot \cos \frac {\pi}{3} = 229.$$

Thus, the $X = \sqrt{229}$ cm.

Answer: $X = \sqrt{229}$ cm.