A particle is subjected to two mutually perpendicular SHM such that x = 2sinωt and

y = 2 sinωt + π2The path of the particle will be

1.  An ellipse

2.  A straight line

3.  A parabola

4.  A circle

Subtopic:  Simple Harmonic Motion |
 59%
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Suppose that a pendulum clock is carried to a depth of 32 km inside the earth (Radius R = 6400 km). To have the correct time from the clock, by what percentage the effective length of the pendulum should be changed? 

1.  0.5%

2.  -0.5%

3.  1%

4.  -1.0%

Subtopic:  Simple Harmonic Motion |
 60%
From NCERT
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When a periodic force \(\vec{F_1}\) acts on a particle, the particle oscillates according to the equation \(x=A\sin\omega t\). Under the effect of another periodic force \(\vec{F_2}\), the particle oscillates according to the equation \(y=B\sin(\omega t+\frac{\pi}{2})\). The amplitude of oscillation when the force (\(\vec{F_1}+\vec{F_2}\)) acts are:

1. \(A+B\) 2. \(\sqrt{A^2+B^2}\)
3. \(\large\frac{\sqrt{A^2+B^2}}{2}\) 4. \(\sqrt{AB}\)
Subtopic:  Simple Harmonic Motion |
 91%
From NCERT
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A particle is executing SHM with amplitude A and angular frequency ω. The time taken by the particle to move from x = 0 to x = A/2 is

1.  π12 ω

2.  π6 ω

3.  π3 ω

4.  πω

Subtopic:  Simple Harmonic Motion |
 82%
From NCERT
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A spring-block system oscillates with a time period \(T\) on the earth's surface. When the system is brought into a deep mine, the time period of oscillation becomes \(T'.\) Then one can conclude that:
1. \(T'>T\)
2. \(T'<T\)
3. \(T'=T\)
4. \(T'=2T\)

Subtopic:  Combination of Springs |
 66%
From NCERT
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A particle executes simple harmonic oscillations under the effect of small damping. If the amplitude of oscillation becomes half of the initial value of 16 mm in five minutes, then what will be the amplitude after fifteen minutes?

1.  8 mm

2.  4 mm

3.  2 mm

4.  1 mm

Subtopic:  Damped Oscillations (OLD NCERT) |
 72%
From NCERT
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Which of the following is incorrect about simple harmonic oscillations of a particle? 
1. force and acceleration differ in phase by the angle of \(90^\circ.\) 
2. force varies linearly with displacement.
3. velocity is \(90^\circ\) ahead in phase relative to displacement from the mean position.
4. K.E. is zero at the extreme position(s).

Subtopic:  Energy of SHM |
 75%
From NCERT
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For a particle executing SHM, the graph between its momentum and displacement will be

1. Straight line

2. Hyperbola

3. Parabola

4. Ellipse

Subtopic:  Simple Harmonic Motion |
 56%
From NCERT
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A particle executes SHM of amplitude 10 m and period 4 s along a straight line. The velocity of the particle at a distance of 6 m from the mean position is: 

1.  2π m/s

2.  4π m/s 

3.  6π m/s

4.  5.4π m/s

Subtopic:  Simple Harmonic Motion |
 86%
From NCERT
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A uniform rod of mass m and length L pivoted from its one end is executing SHM with time period T. If rod suddenly breaks from the middle while passing through its mean position, then the time period of oscillation of remaining half part will be

1.  2T

2.  T2

3.  2T

4.  T2

Subtopic:  Angular SHM |
 66%
From NCERT
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