The 15 g head of a bobble-head doll oscillates in SHM at a frequency of 4.0 Hz.

a. What is the spring constant of the spring on which the head is mounted?

b. suppose the head is pushed 2.0 cm against the spring, then released. What is the head's maximum speed as it oscillates?

c. the amplitude of the head's oscillations decreases to 0.5cm in 4.0s. What is the head's damping constant?

(a) 9.375 N/m

(b) 0.5024 m/s

(c) 0.01 kg/s

Explanation:

mass of head, m = 15 g = 0.015 kg

frequency, f = 4 Hz

Time period, T = 1 / f = 0.25 s

Let k is the spring constant.

(a)

The formula for the time period is

K = 9.375 N/m

(b)

Amplitude, A = 2 cm

Let ω is the angular velocity.

Maximum velocity, v = A ω = A x 2πf

v = 0.02 x 2 x 3.14 x 4 = 0.5024 m/s

(c)

Let b is the damping constant.

A(t = 4s) = 0.5 cm

Ao = 2 cm

Using the formula of damping

Taking natural log on both the sides

ln (0.25) = - 133.3 b

- 133.3 b = - 1.386

b = 0.01 kg/s

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement

i believe the answer is a hope it and is correct