A 3.00 kg block is attached to a spring with force constant k= 150 N/m. The bloc

Question

A 3.00 kg block is attached to a spring with force constant k= 150 N/m. The block is given an initial velocity in the positive direction of magnitude v = 12.0 m/s and no initial displacement. Find (a) the amplitude (b) the phase angle and (c) the frequency. (D) Write a specific equation for the position as a function of time A 3.00 kg block is attached to a spring with force constant k= 150 N/m. The block is given an initial velocity in the positive direction of magnitude v = 12.0 m/s and no initial displacement. Find (a) the amplitude (b) the phase angle and (c) the frequency. (D) Write a specific equation for the position as a function of time A 3.00 kg block is attached to a spring with force constant k= 150 N/m. The block is given an initial velocity in the positive direction of magnitude v = 12.0 m/s and no initial displacement. Find (a) the amplitude (b) the phase angle and (c) the frequency. (D) Write a specific equation for the position as a function of time

Explanation / Answer

a) Let A is the amplitude.

ApplyEnergy conservation

Initial kinetic energy = final potential energy

0.5*m*v^2 = 0.5*k*A^2

==> A = v*sqrt(m/k)

= 12*sqrt(3/150)

= 1.7 m

b) Initial phase is zero

c) f = sqrt(k/m)/(2*pi)

= sqrt(150/3)/(2*pi)

= 1.13 Hz

d) x(t) = A*sin(w*t)

= 1.7*sin(2*pi*f*t)

= 1.7*sin(2*pi*1.13*t)

= 1.7*sin(7.07*t)

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