Can someone help and answer all the questions? A block with mass M = 3.4 kg is c
ID: 1490666 • Letter: C
Question
Can someone help and answer all the questions?
A block with mass M = 3.4 kg is connected to two springs with force constants k_1 = 50 N/m and k_2 = 113 N/m. The mass moves on a frictionless horizontal surface where it is displaced from equilibrium and released. In both cases below, the motion can be described not only by all the individual forces acting in the problem but also by an equivalent or effective spring constant k_off. In the case shown as 'a' in the figure. What is the effective spring constant k_eff (N/m)? What is the period of the motion (s)? In the case shown as 'b' in the figure, What is the effective spring constant k_eff (N/m)? What is the period of the motion (s)?Explanation / Answer
CASE A
They are in parallel the effective spring constant is given by ;
K = k1 + k2
Period, T = 2pi(m/K) = 2pi(m/(k1 + k2))
CASE B
Consider if you have two springs in series--k1 and k2.
Apply a force F.
k1 compresses a distance F/k1, k1 compresses a distance F/k2
The total compression is F(1/k1 + 1/k2)
So the effective spring constant K is 1 / (1/k1 + 1/k2) = k1 k2 / (k1 + k2), which is less than either k1 or k2.
Period, T = 2pi(m/K) = T = 2pi(m(k1 + k2) / k1 k2)