JEE Mains · Physics · STD 11 - Oscillations
- JEE Mains 2018
- Hard
- MCQ
A particle executes simple harmonic motion and is located at \(x = a, b\) and \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\frac{1}{{2\pi {t_0}}}\cos {\,^{ - 1}}\left( {\frac{{a + c}}{{2b}}} \right)\)
Step-by-step Solution
Detailed explanation
Using \(\mathrm{y}=\mathrm{A} \sin \omega \mathrm{t}\)
\(\mathrm{a}=\mathrm{A} \sin \omega \mathrm{t}_{0}\)
\(b=A \sin 2 \omega t_{0}\)
\(c=A \sin 3 \omega t_{0}\)
\(\mathrm{a}+\mathrm{c}=\mathrm{A}\left[\sin \omega \mathrm{t}_{0}+\sin 3 \omega t_{0}\right]\)\(=2 \mathrm{A} \sin 2 \omega \mathrm{t}_{0}\cos \omega t_{0}\)
\(\frac{a+c}{b}=2 \cos \omega t_{0}\)
\(\Rightarrow \omega=\frac{1}{t_{0}} \cdot \cos ^{-1}\left(\frac{a+c}{2 b}\right)\)
\( \Rightarrow f=\frac{1}{2 \pi t_{0}} \cos ^{-1}\left(\frac{a+c}{2 b}\right)\)
More questions from Physics
- An insulated cylinder of volume \( 60\,cm^{3} \) is filled with a gas at \( 27^{\circ}C \) and 2 atmospheric pressure. Then the gas is compressed making the final volume as \( 20\,cm^{3} \) while allowing the temperature to rise to \( 77^{\circ}C \). The final pressure is __________atmospheric pressure.JEE Mains 2026 Medium
- Two coaxial discs, having moments of inertia \(I_1\) and \(\frac{I_1}{2}\) are a rotating with respectively angular velocities \(\omega_1\) and \(\frac{\omega_1}{2}\), about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f -E_i)\) isJEE Mains 2019 Hard
- An electric field \(\overrightarrow{\mathrm{E}}=4 \mathrm{x} \hat{\mathrm{i}}-\left(\mathrm{y}^{2}+1\right) \hat{\mathrm{j}}\; \mathrm{N} / \mathrm{C}\) passes through the box shown in figure. The flux of the electric field through surfaces \(A B C D\) and \(BCGF\) are marked as \(\phi_{I}\) and \(\phi_{\mathrm{II}}\) respectively. The difference between \(\left(\phi_{\mathrm{I}}-\phi_{\mathrm{II}}\right)\) is (in \(\left.\mathrm{Nm}^{2} / \mathrm{C}\right)\)
JEE Mains 2020 Medium - For an object placed at a distance \(2.4\,m\) from a lens, a sharp focused image is observed on a screen placed at a distance \(12\,cm\) from the lens. A glass plate of refractive index \(1.5\) and thickness \(1\,cm\) is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen \(\dots\,m\)JEE Mains 2022 Hard
- An \(L-\) shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If \(AB = BC\), and the angle made by \(AB\) with downward vertical is \(\theta\) then
JEE Mains 2019 Hard - Three identical coils \(C _1, C _2\) and \(C _3\) are closely placed such that they share a common axis.\(C _2\) is exactly midway.\(C _1\) carries current I in anti-clockwise direction while \(C _3\) carries current I in clockwise direction. An induced current flows through \(C _2\), will be in clockwise direction whenJEE Mains 2026 Medium
More PYQs from JEE Mains
- In an octagon \(ABCDEFGH\) of equal side, what is the sum of \(\overrightarrow{ AB }+\overrightarrow{ AC }+\overrightarrow{ AD }+\overrightarrow{ AE }+\overrightarrow{ AF }+\overrightarrow{ AG }+\overrightarrow{ AH }\) if, \(\overrightarrow{ AO }=2 \hat{ i }+3 \hat{ j }-4 \hat{ k }\)
JEE Mains 2021 Hard - Magnetic materials used for making permanent magnets \((P)\) and magnets in a transformer \((T)\) have different properties of the following, which property best matches for the type of magnet required \(?\)JEE Mains 2020 Medium