A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance X. Now the combined mass will oscillate on the spring with period

Question

A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance X. Now the combined mass will oscillate on the spring with period (A) T= 2π √(mg/X(M+m)) (B) T= 2π √(X(M+m)/mg) (C) T= (π/2) √(X(M+m)/mg) (D) T= 2π √((M+m)/mg)

Tardigrade Admin · Accepted Answer

Time period of spring block system is given by,

T = 2 π \frac{ma ss o f b l oc k}{s p r in g co n s t an t}

Here, mass of block =

(M + m)

Spring constant

k = \frac{m g}{X}

[∵ A t e q u i l ib r i u m, (M + m) g = k (X_{0} + X) or, m g = k X (I ni t ia ll y, M g = k X_{0})]

∴ T = 2 π \frac{( M + m )}{\frac{m g}{X}} = 2 π \frac{( M + m ) X}{m g}

Q. A mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $X$ . Now the combined mass will oscillate on the spring with period

$T = 2 π \frac{m g}{X ( M + m )}$

$T = 2 π \frac{X ( M + m )}{m g}$

$T = \frac{π}{2} \frac{X ( M + m )}{m g}$

$T = 2 π \frac{( M + m )}{m g}$

Q. A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance X. Now the combined mass will oscillate on the spring with period

T=2πX(M+m)mg​​

T=2πmgX(M+m)​​

T=2π​mgX(M+m)​​

T=2πmg(M+m)​​

Time period of spring block system is given by, T=2πspringconstantmassofblock​​ Here, mass of block = (M+m) Spring constant k=Xmg​ [∵Atequilibrium,(M+m)g=k(X0​+X)or,mg=kX(Initially,Mg=kX0​)] ∴T=2πXmg​(M+m)​​=2πmg(M+m)X​​

Q. A mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $X$ . Now the combined mass will oscillate on the spring with period

$T = 2 π \frac{m g}{X ( M + m )}$

$T = 2 π \frac{X ( M + m )}{m g}$

$T = \frac{π}{2} \frac{X ( M + m )}{m g}$

$T = 2 π \frac{( M + m )}{m g}$