Question

if 1 Kg mass is displaced 4 cm downward from its equilibrium position and if it
oscillates 20 times in 40 seconds, spring constant is:​

Answer 1

Given that,

Mass = 1 kg

Number of oscillation = 20

Time = 40 sec

Displacement = 4 cm

If 1 Kg mass is displaced 4 cm downward from its equilibrium position

(a). We need to calculate the spring constant

Using formula of spring constant

$k=\dfrac{mg}{x}$

Put the value into the formula

$k=\dfrac{1\times9.8}{4\times10^{-2}}$

$k=245\ N/m$

(b). If it oscillates 20 times in 40 seconds

We need to calculate the time period

Using formula of time period

$T=\dfrac{t}{N}$

Where, t = time

N = Number of oscillation

Put the value into the formula

$T=\dfrac{40}{20}$

$T=2\ sec$

We need to calculate the spring constant

Using formula of time period

$T=2\pi\sqrt{\dfrac{m}{k}}$

Where, m = mass

k =spring constant

$2=2\pi\sqrt{\dfrac{1}{k}}$

$4=4\pi^2\times\dfrac{1}{k}$

$k=\pi^2$

$k=9.86\ kg/s^2$

Hence, The spring constant is 245 N/m.

The spring constant is 9.86 kg/s².