AP EAMCET · PHYSICS · Oscillations
The displacement of a damped harmonic oscillator is given by \(x(\mathrm{t})=\mathrm{e}^{-0.1 \mathrm{t}} \cos (10 \pi \mathrm{t}+\varphi)\). Here \(\mathrm{t}\) is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:
- A \(27 \mathrm{~s}\)
- B \(4 \mathrm{~s}\)
- C \(13 \mathrm{~s}\)
- D \(7 \mathrm{~s}\)
Answer & Solution
Correct Answer
(D) \(7 \mathrm{~s}\)
Step-by-step Solution
Detailed explanation
Amplitude \(A=A_0 e^{-k t}\) From given condition, \(\frac{A_0}{2}=A_0 e^{-0.1 \times t}\) \[ \begin{aligned} & \Rightarrow \ln 2=0.1 \times t \\ & t=\frac{\ln 2}{0.1}=\frac{0.693}{0.10}=6.935 \approx 7 \mathrm{~s} \end{aligned} \]
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
- The volume of a gas at \(30^{\circ} \mathrm{C}\) temperature and \(760 \mathrm{~mm}\) of \(\mathrm{Hg}\) pressure is \(100 \mathrm{cc}\). Then its volume at the same temperature and \(400 \mathrm{~mm}\) of \(\mathrm{Hg}\) isAP EAMCET 2022 Easy
- Assertion (A) The velocity of a projectile at
a point on its trajectory is equal to the slope at
that point.
Reason (R) The velocity vector at a point
always along the tangent to the trajectory at
that point.AP EAMCET 2018 Easy - An amplitude modulate wave is represented by \(10\left[1+0.6 \sin \left(40 \times 10^3 t\right)\right] \sin \left(4 \times 10^6 t\right)\) volt where \(t\) is in seconds. Then the ratio of the upper to the lower side band frequencies isAP EAMCET 2023 Medium
- The magnitude of an electric field which can just suspend a deuteron of mass \(3.2 \times 10^{-27} \mathrm{~kg}\) freely in air isAP EAMCET 2024 Easy
- Two particles of equal mass ' \(m\) ' and equal charge ' \(q\) ' are separated by a distance of 16 cm . They do not experience any force. The value of \(\frac{q}{m}\) is _____ (if ' \(G\) ' is the universal gravitational constant and ' \(g\) ' is the acceleration due to gravity).AP EAMCET 2024 Easy
- Four resistors \(A, B, C\) and \(D\) form a Wheatstones bridge. The bridge is balanced, when \(C=100 \Omega\). If \(A\) and \(B\) are interchanged, the bridge balances for \(C=121 \Omega\). The value of \(D\) isAP EAMCET 2012 Easy
More PYQs from AP EAMCET
- The value of \(c\) for which the Lagrange's mean value theorem is applicable for the function \(f(x)=x(x+3)(x-2)\) in \([-1,4]\), isAP EAMCET 2017 Easy
- If \(\mathbf{P}=3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{Q}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) are two sides of a triangle, then its area is equal to ____ sq units.AP EAMCET 2020 Easy
- \(K_p\) for the conversion of oxygen to ozone at \(400 \mathrm{~K}\) is \(1.0 \times 10^{-30}\), its standard Gibbs energy change in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is approximatelyAP EAMCET 2019 Medium
- Bag A contains 3 white and 4 red balls, bag B contains 4 white and 5 red balls and bag \(C\) contains 5 white and 6 red balls. If one ball is drawn at random from eath of these three bags, then the probability of getting one white and two red balls isAP EAMCET 2024 Medium
- A window used to thermally insulate a room from outside consists of two parallel glass sheets each of area \(2.6 \mathrm{~m}^2\) and thickness \(1 \mathrm{~cm}\) separated by \(5 \mathrm{~cm}\) thick stagnant air. In the steady state, the room glass interface is at \(18^{\circ} \mathrm{C}\) and the glass-outdoor interface is at \(-2{ }^{\circ} \mathrm{C}\). If the thermal conductivities of glass and air are respectively \(0.8 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}\) and \(0.08 \mathrm{Wm}^{-1} \mathrm{~K}^{-1}\), the rate of flow of heat through the window isAP EAMCET 2019 Hard
- If \(a \neq 0\) and the line \(2 b x+3 c y+4 d=0\), passes through the points of intersection of the parabolas \(y^2=4 a x\) and \(x^2=4 a y\), thenAP EAMCET 2022 Hard