First slide

Simple hormonic motion

Question

A block P of mass m is placed on a frictionless other 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 l. The maximum value of the friction force between P and Q is:

Moderate

A

kA
B

$\frac{kA}{2}$
C

zero
D

$μ_{s} mg$

Solution

$f_{\max} = {mω}^{2} A$
With $ω^{2} = \frac{k}{m + m} = \frac{k}{2 m}$
Hence, $f_{\max} = m (\frac{k}{2 m}) A = \frac{kA}{2}$

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