First slide

Simple hormonic motion

Question

A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure, µ_s is the coefficient of friction between P
and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is

Moderate

A

kA
B

kA/2
C

zero
D

µ_smg

Solution

Let Q is displaced through a small distance x. Now force exerted by spring on Q is k x If the initial acceleration of the system be A, then
$\begin{array}{lll} kx - f & = mA . . . (1) for the upper block \\ further & f & = mA . . . (2) for the lower block \\ ∴ & kx - mA & = mA or kx = 2 mA \\ or & A & = (kx / 2 m) \end{array}$
From eq. (2), f =(m k x /2 m) = (k x /2).

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