a mass of 4 kg is attached to a spring and its disposal cement is described by t

Question

a mass of 4 kg is attached to a spring and its disposal cement is described by the equation: x=7cos(3t+pi/4) where x is in meters a t is in seconds. A. Find the max acceleration of the mass. B. Find the period of oscillation. C. Find the velocity of the mass at t=1.4s. D. Find the value of the spring constant k. E. Find at what positive time t the velocity first becomes zero. F. Find the force acting on the arrival at t=2s. a mass of 4 kg is attached to a spring and its disposal cement is described by the equation: x=7cos(3t+pi/4) where x is in meters a t is in seconds. A. Find the max acceleration of the mass. B. Find the period of oscillation. C. Find the velocity of the mass at t=1.4s. D. Find the value of the spring constant k. E. Find at what positive time t the velocity first becomes zero. F. Find the force acting on the arrival at t=2s. A. Find the max acceleration of the mass. B. Find the period of oscillation. C. Find the velocity of the mass at t=1.4s. D. Find the value of the spring constant k. E. Find at what positive time t the velocity first becomes zero. F. Find the force acting on the arrival at t=2s.

Explanation / Answer

angular speed w = 3 rad/s

Amplitude A = 7m

A) amax = w^2*A = 63 m/s^2

B) T = 2pi/w = (6.28)/3 = 2.093 s

C) v = -w*A*sin(wt + phi )

v = -A*w*sin(3t+pi/4)

at t = 1.4

v = -7*3*sin((3*1.4)+(3.14/4))

v = -20.22 m/s

D) K = m*w^2 = 4*3*3 = 36 N/m

E) v = 0 = A*w*sin(3t+pi/4)

3t + pi/4 = pi

3t = 3pi/4 =

t = pi/4 = 3.14/4 = 0.785 s

F) x = 7*cos(6+(3.14/4)) = 6.14 m

F = k*x = 36*6.14 = 221.04 N

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