a block of mass 12.0 kg is connected to a spring on a horizontal frictionless su

ID: 3899773 • Letter: A

Question

a block of mass 12.0 kg is connected to a spring on a horizontal frictionless surface. The spring constant is 200N/m. the block-spring system undergoes simple harmonic motion.

at a time t=0, the position of the block x= -80.0 cm and its velocity Vx-3.65m/s
a) determine the angular frequency and period of the motion b) determine the amplitude c) determine the phase angle d) write the expression for the position of the block as the function of time e) determine the position at time =3.00s f) determine the velocity at time =3.00s g) determine the acceleration at time =3.00s at a time t=0, the position of the block x= -80.0 cm and its velocity Vx-3.65m/s
a) determine the angular frequency and period of the motion b) determine the amplitude c) determine the phase angle d) write the expression for the position of the block as the function of time e) determine the position at time =3.00s f) determine the velocity at time =3.00s g) determine the acceleration at time =3.00s

Explanation / Answer

given M =12 kg K =200N/m

at t = 0 x = -80.cm Vx = -3.65 m/sec

a. angular frequency (w) = squrt (K/M) = 4.08 /sec

period of motion (T) = 2x3.14squrt (m/k) = 1.54 sec.

b. Amplitude (A) = V/w = 0.894 m

c.phase angle : at t =0 x= -.80

let X = A cos(wt + theta)

- 0.8 = 0.894cos(theta)

phase angle = 153.5 degrees.

d. X = 0.894 cos (4.08t + 153.5)

e. at t = 3sec.

X = -0.8664

f. velocity (v) = dx/dt = 3.647 m/sec

g. accleration (a) = dv/dt = -14.42 m/sec^2

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a block of mass 12.0 kg is connected to a spring on a horizontal frictionless su

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