# When a mass is suspended separately by two different springs, in successive order, then the time period of oscillations is $$t _1$$ and $$t_2$$ respectively. If it is connected by both springs as shown in the figure below, then the time period of oscillation becomes $$t_0.$$ The correct relation between $$t_0,$$ $$t_1$$ & $$t_2$$ is: 1. ${{\mathrm{t}}_{0}}^{2}={{\mathrm{t}}_{1}}^{2}+{{\mathrm{t}}_{2}}^{2}$ 2. ${{\mathrm{t}}_{0}}^{-2}={{\mathrm{t}}_{1}}^{-2}+{{\mathrm{t}}_{2}}^{-2}$ 3. ${{\mathrm{t}}_{0}}^{-1}={{\mathrm{t}}_{1}}^{-1}+{{\mathrm{t}}_{2}}^{-1}$ 4. ${\mathrm{t}}_{0}={\mathrm{t}}_{1}+{\mathrm{t}}_{2}$

Subtopic:  Combination of Springs |
69%
From NCERT
AIPMT - 2002
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The displacement between the maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is:
1. $$\pm \frac{a}{2}$$
2. $$+a$$
3. $$\pm a$$
4. $$-1$$

Subtopic:  Energy of SHM |
74%
From NCERT
AIPMT - 2002
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The time period of a mass suspended from a spring is $$T$$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be:
1. $$\frac{T}{4}$$
2. $$T$$
3. $$\frac{T}{2}$$
4. $$2T$$

Subtopic:  Spring mass system |
73%
From NCERT
AIPMT - 2003
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A particle of mass $$m$$ oscillates with simple harmonic motion between points $$x_1$$ and $$x_2$$, the equilibrium position being $$O$$. Its potential energy is plotted. It will be as given below in the graph:

 1 2 3 4
Subtopic:  Energy of SHM |
84%
From NCERT
AIPMT - 2003
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The potential energy of a simple harmonic oscillator, when the particle is halfway to its endpoint, will be:
1. $$\frac{2E}{3}$$
2. $$\frac{E}{8}$$
3. $$\frac{E}{4}$$
4. $$\frac{E}{2}$$

Subtopic:  Energy of SHM |
80%
From NCERT
AIPMT - 2003
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A body oscillates with SHM according to the equation (in SI units), $$x= 5\cos\left[2\pi t +\frac{\pi}{4}\right].$$ At $$t = 1.5$$ s, acceleration of the body will be:
 1 $$140 \text{ cm} / \text{s}^2$$ 2 $$160 \text{ m} / \text{s}^2$$ 3 $$140 \text{ m} / \text{s}^2$$ 4 $$14 \text{ m} / \text{s}^2$$
Subtopic:  Linear SHM |
58%
From NCERT
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The frequency of a simple pendulum in a free-falling lift will be:
1. zero
2. infinite
3. can't say
4. finite

Subtopic:  Angular SHM |
67%
From NCERT
AIPMT - 1999
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A spring elongates by a length 'L' when a mass 'M' is suspended to it. Now a tiny mass 'm' is attached to the mass 'M' and then released. The new time period of oscillation will be:

1.  $$2 \pi \sqrt{\frac{\left(\right. M + m \left.\right) l}{Mg}}$$

2. $$2 \pi \sqrt{\frac{ml}{Mg}}$$

3. $$2 \pi \sqrt{L / g}$$

4. $$2 \pi \sqrt{\frac{Ml}{\left(\right. m + M \left.\right) g}}$$

Subtopic:  Spring mass system |
59%
From NCERT
AIPMT - 1999
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Which one of the following statements is true for the speed $$v$$ and the acceleration $$a$$ of a particle executing simple harmonic motion?
 1 The value of $$a$$ is zero whatever may be the value of $$v$$. 2 When $$v$$ is zero, $$a$$ is zero. 3 When $$v$$ is maximum, $$a$$ is zero. 4 When $$v$$ is maximum, $$a$$ is maximum.
Subtopic:  Simple Harmonic Motion |
86%
From NCERT
AIPMT - 2004
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The frequency of a spring is $$n$$ after suspending mass $$M.$$ Now, after mass $$4M$$ mass is suspended from the spring, the frequency will be:
 1 $$2n$$ 2 $$n/2$$ 3 $$n$$ 4 none of the above
Subtopic:  Spring mass system |
81%
From NCERT
AIPMT - 1998
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