Both are similar, please help me. I am terrible with relating equations and find

Question

Both are similar, please help me. I am terrible with relating equations and finding x values without actually plugging in for numbers.

At t=0, an oscillator is started with zero velocity at its maximum positive amplitude xm. The equation for simple harmonic motion is

x(t) = xmcos(?t + ?)

What is the value of ??

At t = 0, an oscillator is started with maximum negative velocity at x(0) = 0. The equation for simple harmonic motion is

x(t) = xmcos(?t + ?)

What is the value of ??

At t = 0, an oscillator is started with zero velocity at its maximum positive amplitude xm. The equation for simple harmonic motion is x(t) = xmcos(omega t + phi) What is the value of phi? 0 +pi/4 -pi/4 +pi/2 ?pi/2 none of the above At t = 0, an oscillator is started with maximum negative velocity at x(0) = 0. The equation for simple harmonic motion is x(t) = xmcos(omega t + phi) What is the value of phi? 0 +pi/4 -pi/4 +pi/2 ?pi/2 none of the above

Explanation / Answer

1) Since it is given maximum positive amplitude

At t= 0 , maximum amplitude is xm , cos(0) = 1 , So x(0) = xm

hence answer is Option A : 0

2) Since it is goven maximum negative velocity

x(t) = xm cos(wt + phi )

v(t) = dx/dt = -xm * w sin (wt + phi )

At t = 0 , v(0) = -xm *w is maximum negative value , it is possible at sin(phi) = 1 therefore phi = pi/2

Hence answer is Option E : -pi/2

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