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Question-132265




Question Number 132265 by Salman_Abir last updated on 12/Feb/21
Answered by physicstutes last updated on 12/Feb/21
m = 4 kg, k = 100 Nm^(−1)    T = 2π(√(m/k)) = 2π(√(4/(100)))   ⇒ T = ((4π)/(25)) s  f = (1/T) = ((25)/(4π)) Hz  T = ((2π)/ω) ⇒ ω = ((2π)/T)  = 2π . ((25)/(4π)) = ((25)/2) rad/s
$$\mathrm{m}\:=\:\mathrm{4}\:\mathrm{kg},\:{k}\:=\:\mathrm{100}\:\mathrm{Nm}^{−\mathrm{1}} \\ $$$$\:{T}\:=\:\mathrm{2}\pi\sqrt{\frac{{m}}{{k}}}\:=\:\mathrm{2}\pi\sqrt{\frac{\mathrm{4}}{\mathrm{100}}}\: \\ $$$$\Rightarrow\:{T}\:=\:\frac{\mathrm{4}\pi}{\mathrm{25}}\:\mathrm{s} \\ $$$${f}\:=\:\frac{\mathrm{1}}{{T}}\:=\:\frac{\mathrm{25}}{\mathrm{4}\pi}\:\mathrm{Hz} \\ $$$${T}\:=\:\frac{\mathrm{2}\pi}{\omega}\:\Rightarrow\:\omega\:=\:\frac{\mathrm{2}\pi}{{T}}\:\:=\:\mathrm{2}\pi\:.\:\frac{\mathrm{25}}{\mathrm{4}\pi}\:=\:\frac{\mathrm{25}}{\mathrm{2}}\:\mathrm{rad}/\mathrm{s} \\ $$

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