A system is shown in the figure. The time period for SHM of the two blocks will be:
Both the spring are in series
Keq = k(2k)/k+2k = 2k/3
Time period T = 2π √ μ/Keq
where μ = m1m2/m1 +m2
HERE μ = m/2
T = 2π√ m/2. 3/2k = 2π √3m/4k
Alternative method :
∴ mx = mx ⇒ x = x2
force equation for first block;
2k/3(X1+X2) = m d2x1/dt2
PUT X1 = x2
= d2x1/dt2 + 4k/3m X1 = 0
ω2 = 4k/3m
T = 2π√3m/4k
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