14.10 Simple Harmonic Motion Quiz. A 1.6 kg block moving with a speed of 0.s m/s

Question

14.10 Simple Harmonic Motion Quiz. A 1.6 kg block moving with a speed of 0.s m/s on a horizontal, frictionless surface strikes a spring of constant 250 N/m. The block becomes attached to the spring and SHM ensues I. 2? Determine the angular frequency constant, frequency and period of the SHM 2. Determine the amplitude, maximum velocity and acceleration, and the total energy of the system. Determine the location, velocity, and acceleration of the block 1.8 seconds after striking the spring. 3. Assume that when the block is at its equilibrium position. a ball of putty of equal mass is dropped on the block. How would the total energy, the amplitude, and the period be affected? Hint: Think of the drop as a collision. What's conserved? 4. 5. Assume that when the block is at its maximum position, a ball of putty of equal mass is dropped on the block. How would the total energy, the amplitude, and the period be affected? Hint: Think of the drop as a collision. What's conserved?

Explanation / Answer

1. w = sqrt( k / m ) = sqrt(250 / 1.6)

w = 12.5 rad/s .....Ans

f = w / 2pi = 2 Hz

T = 1/f = 0.50 sec ....Ans

2. v_max = 0.5 m/s

and v_max = w A

A = 0.04 m Or 4 cm .....Ans

v_max = 0.5 m/s .....Ans

a_max = A w^2 = 6.25 m/s^2 ....Ans

TE = m v_max^2 /2 Or k A^2 / 2

Te = 0.20 J ....Ans

3. x = - (0.04)sin(12.5t)

at 1.8 s

x = 0.02 m right to initial position

v = dx/dt = - 0.5 cos(12.5t)

v = 0.44 m/s

Ans: 0.44 m/s to the right

a = dv/dt = 6.25 sin(12.5t)

a = - 3.04 m/s^2

Ans: 3 m/s^2 to the left

4. mass increases so time period increases.

and speed decreases so total energy, amplitude decreases.

5. period - increases.

total energy remains constant.

ampitude also remains constant

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