1. Tardigrade
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  3. Physics
  4. A mass M, attached to a spring, oscillates with a period of 2 s. If the mass is increased by 4 kg, the time period increases by 1 s. Assuming that Hooke's law is obeyed, the initial mass M was

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Q. A mass $M$, attached to a spring, oscillates with a period of $2 \,s$. If the mass is increased by $4 \,kg$, the time period increases by 1 s. Assuming that Hooke's law is obeyed, the initial mass $M$ was

Oscillations

Solution:

$As , T=2=2 \pi \sqrt{\frac{M}{k}}$
$2+1=2 \pi \sqrt{\frac{M+4}{k}}$ (from questions)
or $3=2 \pi \sqrt{\frac{k+4}{k}}$
So, $\frac{4}{9}=\frac{M}{M+4}$
or $4 \,M+16=9 M$
or $M=\frac{16}{5}=3.2\,kg$