the missing numbr [07] = 121 N/m, so put in 121 and please answer all parts A bl

Question

the missing numbr [07] = 121 N/m, so put in 121 and please answer all parts

A block with mass M = 3.4 kg is connected to two springs with force constants k_1 = 50 N/m and k_2 = [07] ___ 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_eff. In the case shown as 'a' in the figure, (a) What is the effective spring constant k_eff (N/m)? (b) What is the period of the motion (s)? In the case shown as 'b' in the figure, (c) What is the effective spring constant k_eff(N/m)? (d) What is the period of the motion (s)?

Explanation / Answer

Given that

mass M=3.4 kg

spring constant K1=50 N/m

spring constant K2=121 N/m

case (a)

now we find the effective spring constant

the effective spring constant Keff=50+121=171 N/m

now we find the time period

the time period T=2*3.14*[3.4/171]^1/2=0.89 sec

case (b)

now we find the effective spring constant

Keff=50*121/121+50=35.4 N/m

now we find the time period

time period T=2*3.14*[3.4/35.4]^1/2=1.95 sec

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