First slide

Applications of SHM

Question

A spring of spring constant k is cut into n equal parts, out of which r parts are placed in parallel and connected with mass M. The time period of oscillatory motion of mass M is

Moderate

A

$T = 2 π \sqrt{\frac{M}{n r k}}$
B

$T = 2 π \sqrt{\frac{n r M}{k}}$
C

$T = 2 π \sqrt{\frac{r M}{n k}}$
D

$T = 2 π \sqrt{\frac{n M}{r k}}$

Solution

$k \cdot l = k^{'} \times \frac{l}{n} = constant$
New spring constant for each part is $k^{'} = n k$
Now r part are taken in Parallel.
$so k_{eq} = n r k$
$Time period = 2 π \sqrt{\frac{M}{k_{eq}}} = 2 π \sqrt{\frac{M}{n r k}}$

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