At equilibrium, the springs are released, mass M is oscillating under the influence of three springs, `k_(1),k_(2)andk_(3)` as shown. Its frequency `(upsilon)` of oscillation is `(1)/(2pi)sqrt((k_(eq))/(M))`, where `k_(eq)` I such that

Options

A. `k_(eq)=k_(1)+k_(2)+k_(3)`
B. `k_(eq)=(k_(1)+k_(2)+k_(3))/(3)`
C. `(1)/(k_(eq))=(1)/(k_(1))+(1)/(k_(2))+(1)/(k_(3))`
D. `k_(eq)=(k_(1)+k_(2)-k_(3))`

Answer

A

Explanation

When the mass M is displaced slightly to the right, the resultant forces acting on the mass M is as shown.
`F_("net")=-(k_(1)+k_(2)+k_(3)).x,`
Thus, `k_(eq)=k_(1)+k_(2)+k_(3)`