MHT CET · Physics · Oscillations
A particle move in S.H.M. such that its acceleration is a \(=-\mathrm{px}\), where ' \(\mathrm{x}\) ' is the displacement of particle from equilibrium position and ' \(\mathrm{p}\) ' is a constant. The period of oscillation is
- A \(2 \pi \sqrt{p}\)
- B \(2 \sqrt{\frac{\pi}{p}}\)
- C \(\frac{2 \pi}{p}\)
- D \(\frac{2 \pi}{\sqrt{p}}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 \pi}{\sqrt{p}}\)
Step-by-step Solution
Detailed explanation
For SHM the acceleration a is proportional to the displacement \(x\) and it is directed towards the mean position of the particle:
\(\mathrm{a}=-\omega^2 \mathrm{x}=-\mathrm{px}\)
where, \(\omega\) is the angular frequency of the SHM.
On comparison, \(\omega=\sqrt{\mathrm{p}}\)
Thus, the period of oscillation can be written as, \(T=\frac{2 \pi}{\omega}=\frac{2 \pi}{\sqrt{p}}\)
\(\mathrm{a}=-\omega^2 \mathrm{x}=-\mathrm{px}\)
where, \(\omega\) is the angular frequency of the SHM.
On comparison, \(\omega=\sqrt{\mathrm{p}}\)
Thus, the period of oscillation can be written as, \(T=\frac{2 \pi}{\omega}=\frac{2 \pi}{\sqrt{p}}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A transformer is a device which convertsMHT CET 2012 Easy
- Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire then the ratio of the lengths of the first wire to second wire isMHT CET 2017 Medium
- \(U\) is the PE of an oscillating particle and \(F\) is the force acting on it at a given instant. Which of the following is true ?MHT CET 2010 Medium
- A metal rod of length \(\mathrm{L}\) and cross-sectional area \(\mathrm{A}\) is heated through \(\mathrm{T}^{\circ} \mathrm{C}\). What is the force required to prevent the expansion of the rod lengthwise?
(Y= Young's modulus of material of the rod, \(\alpha=\) coefficient of linear expansion of
the rod.)MHT CET 2020 Easy - A metal rod has length, cross-sectional area and Young's modulus as ' \(\mathrm{L}^{\prime},{ }^{\prime} \mathrm{A}^{\prime}\) and \(\mathrm{Y}^{\prime}\)
respectively. If the elongation in the rod produced is ' \(\ell^{\prime}\) then work done is proportional toMHT CET 2020 Medium - A ray of light travels from air to water to glass and again from glass to air. Refractive index of water with respect to air is ' \(x^{\prime}\), glass with respect to water is ' \(y^{\prime}\) and air with respect to glass is 'z'. Which one of the following is correct?MHT CET 2020 Easy
More PYQs from MHT CET
- chlorosodium acetate on boiling with aqueous sodium nitrite givesMHT CET 2019 Medium
- \(If \frac{x}{x-y}=\log \left(\frac{a}{x-y}\right), \text { then } \frac{d y}{d x}=\)MHT CET 2020 Easy
- Given below are two statements.
Statement I - Consumption of narcotic -analgesics, anabolic steroids and diuretics decreases muscle strength.
Statement II - In females, the anabolic steroids may lead to masculinization and mood swings.
In the light of above statements, choose the most appropriate answer from the options given below.MHT CET 2022 Medium - Which one of the following statements is wrong?MHT CET 2023 Easy
- The slope of a graph \(\log [A]_t\) versus ' \(t\) ' for first order reaction is \(-2.5 \times 10^{-3} \mathrm{~s}^{-1}\). Find rate constant of the reaction?MHT CET 2025 Easy
- Two simple harmonic motions are represented as \(y_1=10 \sin \omega t\) and \(y_2=10 \sin \omega t+5 \cos \omega t\). The ratio of the amplitudes of \(y_1\) and \(y_2\) isMHT CET 2022 Medium