Question 190: Oscillations

Question

A particle executes simple harmonic motion represented by displacement function as
x(t) = A sin($$\omega$$t + $$\phi$$)
If the position and velocity of the particle at t = 0 s are 2 cm and 2$$\omega$$ cm s
$$-$$1
respectively, then its amplitude is $$x\sqrt 2 $$ cm where the value of x is _________________.

Accepted Answer

x(t) = A sin($$\omega$$t + $$\phi$$)
v(t) = A$$\omega$$ cos ($$\omega$$t + $$\phi$$)
2 = A sin$$\phi$$ ...... (1)
2$$\omega$$ = A$$\omega$$ cos$$\phi$$ ....... (2)
From (1) and (2)
tan$$\phi$$ = 1
$$\phi$$ = 45$$^\circ$$
Putting value of $$\phi$$ in equation (1),
$$2 = A\left\{ {{1 \over {\sqrt 2 }}} ight\}$$
$$A = 2\sqrt 2 $$
$$ 	herefore $$ x = 2

Oscillations

A particle executes simple harmonic motion represented by displacement function as x(t) = A sin($\omegat + \phi) If the position and velocity of the particle at t = 0 s are 2 cm and 2\omega cm s -1 respectively, then its amplitude is x\sqrt 2 $ cm where the value of x is _________________.

Integer / Numeric Answer Type