Question

PROBLEM 3 (10 POINTS) Find the frequency of oscillation of.mass m suspended by two springs having constants ki and k2, in each of the configurations shown below. ki k2

Answer 1

a) This is a series combination of two springs with spring constants k₁ and k₂.

Total spring constant of this system :

a) This is a series combination of two springs with spring constants k_1�and k_2. Total spring constant of this system: 1/k = 1/k_1 + 1/k_2 k = k_1 k_2/k_1 + k_2 The time period of oscillation is given as: T = 2 pi squareroot m/k The frequency of oscillation is inverse of the time period of oscillation: v = 1/T = 1/2 pi squareroot k/m = 1/T = 1/2 pi squareroot k_1 k_2/(k_1 + k_2)/m b) This is the parallel combination of two springs. The overall spring constant of the system is: k = k_1 + k_2 Thus, the frequency of oscillation of mass m is: 1/2 pi squareroot k_1 + k_2/m

The time period of oscillation is given as:

$T=2n$

The frequency of oscillation is inverse of the time period of oscillation:

b) This is the parallel combination of two springs. The overall spring constant of the system is:

k=k₁+k₂

_{Thus, the frequency of oscillation of mass m is:}