TS EAMCET · Physics · Oscillations
If the amplitudes of a damped harmonic oscillator at times \(t=0, t_1\) and \(t_2\) are \(A_0\), \(A_1\) and \(A_2\) respectively, then the amplitude of the oscillator at a time of \(\left(t_1+t_2\right)\) is
- A \(\frac{\mathrm{A}_0+\mathrm{A}_1+\mathrm{A}_2}{3}\)
- B \(\frac{\mathrm{A}_2 \mathrm{~A}_0}{\mathrm{~A}_1}\)
- C \(\frac{\mathrm{A}_1 \mathrm{~A}_0}{\mathrm{~A}_2}\)
- D \(\frac{\mathrm{A}_1 \mathrm{~A}_2}{\mathrm{~A}_0}\)
Answer & Solution
Correct Answer
(D) \(\frac{\mathrm{A}_1 \mathrm{~A}_2}{\mathrm{~A}_0}\)
Step-by-step Solution
Detailed explanation
\(A(t) = A_0 e^{-\gamma t}\) \(A_1 = A_0 e^{-\gamma t_1}\) \(A_2 = A_0 e^{-\gamma t_2}\) \(A(t_1+t_2) = A_0 e^{-\gamma(t_1+t_2)} = A_0 e^{-\gamma t_1} e^{-\gamma t_2}\) \(A(t_1+t_2) = A_0 \left(\frac{A_1}{A_0}\right) \left(\frac{A_2}{A_0}\right) = \frac{A_1 A_2}{A_0}\)
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
- An infinite non-conducting sheet has a surface charge density \(2 \times 10^{-7} \mathrm{C} / \mathrm{m}^2\) on one side. The distance between two equipotential surfaces whose potential differ by \(90 \mathrm{~V}\) is (assume, \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \frac{\mathrm{Nm}^2}{\mathrm{C}^2}\) )TS EAMCET 2020 Medium
- A body is projected at an angle \(\theta\) so that its range is maximum. If \(T\) is the time of flight, then the value of maximum range is (acceleration due to gravity \(=g\) )TS EAMCET 2014 Medium
- Twelve cells, each having emf \(E\) volts are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This 12 cell battery is connected in series with an ammeter, an external resistance \(R\) ohms and a two-cell battery (two cells of the same type used earlier, connected perfectly in series). The current in the circuit when the 12-cell battery and 2-cell battery aid each other is 3A and is \(2 \mathrm{~A}\) when they oppose each other. Then, the number of cells in 12-cell battery that are connected wrongly is :TS EAMCET 2006 Hard
- A conducting sphere \(S_1\) of radius \(r_1\) is connected by a conducting wire to another conducting sphere \(S_2\) of radius \(r_2\), where \(r_1=3 \mathrm{~cm}\) and \(r_2=2\) \(\mathrm{cm}\). Before they are connected, \(s_1\) carries charge of 10 units. The electric potential at the point which is at a distance \(4 \mathrm{~cm}\) from the centre of \(S_1\) and a distance \(3 \mathrm{~cm}\) from the centre of \(S_2\) isTS EAMCET 2018 Hard
- The amplitude of a damped oscillator varies with time as \(\mathrm{A}(\mathrm{t})=\mathrm{A}_{\mathrm{o}} \exp (-\mathrm{bt} / 2 \mathrm{~m})\) where \(\mathrm{b}=70 \mathrm{~g} / \mathrm{s}\) and \(\mathrm{m}=200 \mathrm{~g}\). How long does it take for the mechanical energy to drop to one - fourth of its initial value? \([\) Take \(\ln 2=0.7]\)TS EAMCET 2022 Medium
- In a Zener regulated power supply a Zener diode with \(V_z=6 \mathrm{~V}\) is used for regulation. The load current is \(4 \mathrm{~mA}\) and the unregulated input voltage is \(10 \mathrm{~V}\). To get a Zener current five times the load current the value of series resistor \(R_S\) is nearly
TS EAMCET 2020 Medium
More PYQs from TS EAMCET
- A large metal plate has a surface charge density of . An electron having initial kinetic energy of is moving towards the center of the plate. If the electron stops just before reaching the plate then the initial distance between the electron and the plate is [Take ]TS EAMCET 2022 Medium
- Three parallel wires a, b and c carrying currents \(i_a, i_b\) and \(i_c\) as shown in the figure are placed next to each other.
The magnitude force on a length \(l\) of the wire a, if \(\mathrm{d}_2=2 \mathrm{~d}_1, i_b=i_a\) and \(i_c=4 i_a\) isTS EAMCET 2022 Easy - The refractive index of the material of a double convex lens is 1.5 and its focal length is \(5 \mathrm{~cm}\). If the radii of curvature are equal, the value of the radius of curvature (in \(\mathrm{cm}\) ) isTS EAMCET 2007 Medium
- Consider the following statements regarding digital signals. (i) provide a continuous set of values (ii) represent values as discrete steps (iii) can utilise binary system (iv) are in the form of rectangular waves Then the true statements areTS EAMCET 2023 Medium
- If relative permeability of iron is 5500 , then its susceptibility isTS EAMCET 2020 Easy
- The electric flux from a cube of edge \(l\) is \(\phi\) in an enclosed charge. If the edge of the cube is made \(\frac{2}{3} l\) and the charge enclosed in the cube is doubled, then the electric flux value will beTS EAMCET 2020 Easy