Consider a block of mass m attached to two springs, one on the left with spring constant k1 and one on the right with spring constant k2. each spring is attached on the other side to a wall, and the block slides without friction on a horizontal surface. when the block is sitting at x = 0, both springs are relaxed. write newton’s second law, f = ma, as a differential equation for an arbitrary position x of the block. what is the period of oscillation of this system?

Explanation:

When the block is displaced by x units

F= spring force

two springs are connected parallel

Writing Newtons second law, F = ma

a= x" ( differentiating x w.r.t time twice)

this the standard form of equation of oscillation spring mass system

This is the differential equation, x'' means that double differentiation of x , i.e, x'' is acceleration

since,  Period

therefore,

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