The 10 g head of a bobblehead doll oscillates in SHM at a fr

The 10 g head of a bobble-head doll oscillates in SHM at a frequency fo 4.0 Hz.

(a) What is the spring constant of the spring on which the head is mounted?
N/m

(b) Suppose the head is pushed 1.4 cm against the spring, then released. What is the head\'s maximum speed as it oscillates?
m/s

(c) The amplitude of the head\'s oscillation decreases to 0.5 cm in 3.0 s. What is the head\'s damping constant?

Solution

(a)we know w= sqrt (k/m) here w is angular frequency and k is spring constant.

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

2*3.14*4=sqrt(k/0.01) m=0.01 kg

squaring both sides

631.01=k/0.0001)

k=0.063n/m

(b)if the head is pusshed 1.4 cm then the potential energy stored=1/2 *k*x² =1/2*0.063*1.4*1.4*10^-4

this is converted to K.E. =1/2 mv² =1/2*0.063*1.4*1.4*10^-4

v=3.51*10^-2 m/sec