Question

30. A mass m is connected to two springs, of spring constants k1, and k2. The mass is free to move back and forth without friction. Find the acceleration produced when the mass is moved by an amount x, and find the period of its simple harmonic motion. (Need a formula for an answer).

Answer 1

Note: its not clearly mentioned in the question provided that are the spring arrangement connected in series or parallel, so i'm attempting for both below

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if springs are connected in series

net spring constant,

k = k1 k2 / ( k1 + k2)

acceleration produced

a = k x / m = k1 k2 x / ( m ( k1 + k2))

time period of system

(2 pi / T) ^2 = k/m

T = 2 pi sqrt ( m/k)

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if springs are connected in parallel

k = k1 + k2

acceleration of the system

a = k x / m = ( k1 + k2) x / m

time period

T = 2 pi sqrt( (k1+k2) /m)

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Comment before rate in case any doubt, will reply for sure.. goodluck