A spring stretches by 2 mm when it is loaded with a mass of 200 g

Question

A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are ______ Hz and ______ J, respectively. (Take g = 10 $m / s^{2}$ ) [2026]

Smart Achievers · Accepted Answer

(1)

$K (2 \times 10^{- 3}) = (200 \times 10^{- 3}) (10) \Rightarrow K = 1000$

${(U_{spring})}_{\max} = \frac{1}{2} \times 1000 \times {[4 \times 10^{- 3}]}^{2} = 8 \times 10^{- 3} J$

$T = 2 π \sqrt{\frac{m}{k}} = 2 π \sqrt{\frac{200 \times 10^{- 3}}{10^{3}}}$

$\Rightarrow f = \frac{1}{2 π} \sqrt{\frac{10^{4}}{2}} = \frac{10}{2 π} \sqrt{50} = \frac{5 \sqrt{50}}{π} per sec$

Solution

Q.
A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are Hz and J, respectively. (Take g = 10 $m / s^{2}$ ) [2026]

1 $\frac{5 \sqrt{50}}{π} and 8 \times 10^{- 3}$

2 $\frac{5 \sqrt{50}}{π} and 8$

3 $10 \sqrt{50} and 2 \times 10^{- 3}$

4 $\frac{5 \sqrt{50}}{π} and 16 \times 10^{- 3}$

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Solution

Q. A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are ______ Hz and ______ J, respectively. (Take g = 10 m/s2) [2026]

1 550π and 8×10-3

2 550π and 8

3 1050 and 2×10-3

4 550π and 16×10-3