The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude is $5\, s$. In another $10\, s$ it will decrease to
a times its original magnitude, where $\alpha$ equals
- 0.7
- 0.81
- 0.729
- 0.6
The Correct Option is C
Solution and Explanation
Top Questions on simple harmonic motion
- If \(x=5\sin(\pi i+\frac{\pi}{3})m\) represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are :
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- A mass \(m\) is suspended from a spring of negligible mass and the system oscillates with a frequency \(f_1\).The frequency of oscillations if a mass \(9m\) is suspended from the same spring is \(f_2\). The value of \(\frac{f_1}{f_2}\) is ___.
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- The displacement of a particle executing SHM is given by \( x = 10 \sin\left(\omega t + \frac{\pi}{3}\right) \, \text{m} \). The time period of motion is \( 3.14 \, \text{s} \). The velocity of the particle at \( t = 0 \) is ______ m/s.
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- In simple harmonic motion, the total mechanical energy of the given system is \( E \). If the mass of the oscillating particle \( P \) is doubled, then the new energy of the system for the same amplitude is:
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- The position, velocity, and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 \, \text{m}$, $2 \, \text{ms}^{-1}$, and $16 \, \text{ms}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{x} \, \text{m}$ where $x$ is ______.
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Questions Asked in JEE Main exam
- Let \[\vec{a} = \hat{i} + \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} - 8\hat{j} + 2\hat{k}, \quad \text{and} \quad \vec{c} = 4\hat{i} + c_2\hat{j} + c_3\hat{k} \]be three vectors such that \[\vec{b} \times \vec{a} = \vec{c} \times \vec{a}.\]If the angle between the vector $\vec{c}$ and the vector $3\hat{i} + 4\hat{j} + \hat{k}$ is $\theta$, then the greatest integer less than or equal to $\tan^2 \theta$ is:
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- 10 mL of gaseous hydrocarbon on combustion gives 40 mL of CO\(_2\)(g) and 50 mL of water vapour. The total number of carbon and hydrogen atoms in the hydrocarbon is ______ .
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- If each term of a geometric progression \( a_1, a_2, a_3, \dots \) with \( a_1 = \frac{1}{8} \) and \( a_2 \neq a_1 \), is the arithmetic mean of the next two terms and \( S_n = a_1 + a_2 + \dots + a_n \), then \( S_{20} - S_{18} \) is equal to
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A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:
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- $\textbf{Choose the correct statements about the hydrides of group 15 elements.}$
A. The stability of the hydrides decreases in the order \(\text{NH}_3 > \text{PH}_3 > \text{AsH}_3 > \text{SbH}_3 > \text{BiH}_3\)
B. The reducing ability of the hydrides increases in the order \(\text{NH}_3 < \text{PH}_3 < \text{AsH}_3 < \text{SbH}_3 < \text{BiH}_3\)
C. Among the hydrides, \(\text{NH}_3\) is a strong reducing agent while \(\text{BiH}_3\) is a mild reducing agent.
D. The basicity of the hydrides increases in the order \(\text{NH}_3 < \text{PH}_3 < \text{AsH}_3 < \text{SbH}_3 < \text{BiH}_3\)
Choose the most appropriate from the option given below:- JEE Main - 2024
- p -Block Elements
Concepts Used:
Simple Harmonic Motion
Simple Harmonic Motion is one of the most simple forms of oscillatory motion that occurs frequently in nature. The quantity of force acting on a particle in SHM is exactly proportional to the displacement of the particle from the equilibrium location. It is given by F = -kx, where k is the force constant and the negative sign indicates that force resists growth in x.
This force is known as the restoring force, and it pulls the particle back to its equilibrium position as opposing displacement increases. N/m is the SI unit of Force.
Types of Simple Harmonic Motion
Linear Simple Harmonic Motion:
When a particle moves to and fro about a fixed point (called equilibrium position) along with a straight line then its motion is called linear Simple Harmonic Motion. For Example spring-mass system
Conditions:
The restoring force or acceleration acting on the particle should always be proportional to the displacement of the particle and directed towards the equilibrium position.
- – displacement of particle from equilibrium position.
- – Restoring force
- - acceleration
Angular Simple Harmonic Motion:
When a system oscillates angular long with respect to a fixed axis then its motion is called angular simple harmonic motion.
Conditions:
The restoring torque (or) Angular acceleration acting on the particle should always be proportional to the angular displacement of the particle and directed towards the equilibrium position.
Τ ∝ θ or α ∝ θ
Where,
- Τ – Torque
- α angular acceleration
- θ – angular displacement
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