Question 153: Waves

Question

The motion of a mass on a spring, with spring constant K is as shown in figure.The equation of motion is given by x(t) = A sin$$\omega$$t + B cos$$\omega$$t with $$\omega$$ = $$\sqrt {{K \over m}} $$Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos($$\omega$$t $$-$$ $$\phi$$), where C and $$\phi$$ are :

Accepted Answer

$$C\cos \phi  = x(0)$$
$$tC\omega \sin \phi  = v(0)$$
$${\left[ {{{v(0)} \over \omega }} ight]^2} + {[x(0)]^2} = {C^2}$$
$$	an \phi  = {{v(0)} \over {x(0)\omega }}$$

Answer

$$C = \sqrt {{{2v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi  = {	an ^{ - 1}}\left( {{{x(0)\omega } \over {2v(0)}}} ight)$$

Answer

$$C = \sqrt {{{v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi  = {	an ^{ - 1}}\left( {{{x(0)\omega } \over {v(0)}}} ight)$$

Answer

$$C = \sqrt {{{v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi  = {	an ^{ - 1}}\left( {{{v(0)} \over {x(0)\omega }}} ight)$$

Answer

$$C = \sqrt {{{2v{{(0)}^2}} \over {{\omega ^2}}} + x{{(0)}^2}} ,\phi  = {	an ^{ - 1}}\left( {{{v(0)} \over {x(0)\omega }}} ight)$$

Waves

Choose the correct answer: