A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to B, it returns to B after another 3 s. The time period is

(a)

15 s

(b)

6 s

(c)

12 s

(d)

9 s

A simple pendulum is suspended from the roof of a school bus which moves in a horizontal direction with an acceleration a, then the time period is

(a)

\(T\propto \frac { 1 }{ { g }^{ 2 }+{ a }^{ 2 } } \)

(b)

\(T\propto \frac { 1 }{ \sqrt { { g }^{ 2 }+{ a }^{ 2 } } } \)

(c)

\(T\propto \sqrt { { g }^{ 2 }+{ a }^{ 2 } } \)

(d)

\(T\propto \left( { g }^{ 2 }+{ a }^{ 2 } \right) \)

A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is

(a)

T'= \(\sqrt{2}\)T

(b)

\(T'=\frac { T }{ \sqrt { 2 } } \)

(c)

T'=\(\sqrt{2T}\)

(d)

\(T'=\sqrt { \frac { T }{ 2 } } \)

A simple pendulum has a time period T₁. When its point of suspension is moved vertically upwards according as y = k t², where y is vertical distance covered and k = 1 ms⁻², its time period becomes T₂. Then, \(\frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } } \) is (g = 10 m s⁻²).

(a)

\(\frac{5}{6}\)

(b)

\(\frac{11}{10}\)

(c)

\(\frac{6}{5}\)

(d)

\(\frac{5}{4}\)

A pendulum is hung in a very high building oscillates to and fro motion freely like a simple harmonic oscillator. If the acceleration of the bob is 16 ms⁻² at a distance of 4 m from the mean position, then the time period is

(a)

2 s

(b)

1 s

(c)

2\(\pi\)s

(d)

\(\pi\)s

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

(a)

kgms⁻¹

(b)

kgms⁻²

(c)

kgs⁻¹

(d)

kgs

A particle executes simple harmonic motion and displacement y at time t₀, 2t₀ and 3t₀ are A, B and C, respectively. Then the value of \(\frac{A+C}{2B}\) is 

(a)

cos ωt₀

(b)

cos 2ωt₀

(c)

cos 3ωt₀

(d)

1

The x-t graph of a particle undergoing simple harmonic motion is shown. The acceleration of the particle at t =\(\frac{4}{3}\) is ______________.

(a)

\(\frac { \sqrt { 3 } }{ 32 } \pi \) cm/s²

(b)

\(\frac { -{ \pi }^{ 2 } }{ 32 } \) cm/s²

(c)

\(\frac { { \pi }^{ 2 } }{ 32 } \) cm/s²

(d)

\(\frac { -\sqrt { 3 } }{ 32 } \)

The function x =Asin²ωt + B cos²ωt + c sin rot cos rot represents simple harmonic motion for which of the option?

(a)

for all values of A, B & C (C# 0) (b) \(\frac{r}{10}\)

(b)

A=B, C = 2B

(c)

CA = -B, C = 2B

(d)

all of the above

The displacement of an object attached to a spring & executing SAM is given by x = 2\(\times\)10^-2 cos πt the time at which the speed first occus is ________________.

(a)

0.55 μ

(b)

0.75 μ

(c)

0.125 μ

(d)

0.25 μ

If x, v & a denote the displacement, the velocity & acceleration of a particle executing simple harmonic motion of time period T, then which of the following does not change with time ____________.

(a)

a²t²+4π²v²

(b)

aT/x

(c)

aT+2πv

(d)

aT/v

When the maximum k.E of a simple pendulum is k, then what is its displacement in terms of amplitude a when its K.E. is k/2 ____________.

(a)

a/\(\sqrt{2}\)

(b)

a/2

(c)

a/\(\sqrt{3}\)

(d)

a/3

A spring is cut into 4-equal parts & 2 parts are connected in parallel. What is the effective in parallel. What is the effective spring contest?

(a)

4 k

(b)

16 k

(c)

8 k

(d)

6 k

The ratio of frequences of 2 pendulums are 2 : 3, then their lengths are in ratio ______________.

(a)

\(\sqrt { \frac { 2 }{ 3 } } \)

(b)

\(\sqrt { \frac { 3 }{ 2 } } \)

(c)

\(\frac{4}{9}\)

(d)

\(\frac{9}{4}\)

If a simple pendulum of length 'L' has maximum angular displacement. Then the maximum kinetic energy of bob mass m is ____________.

(a)

\(\frac { 1 }{ 2 } \frac { ML }{ 9 } \)

(b)

\(\frac { Mg }{ 2L } \)

(c)

MgL (1- cos α)

(d)

MgL sinα/2

The phase difference between the unstantaneous velocity & acceleration of a particle executing simple harmonic motion is ________________.

(a)

0.5 π

(b)

π

(c)

0.707π

(d)

0.61 m

Two simple pendulums of time periods 2.0 s & 2.1 s are made to vibrate simultaneously. They are in phase initially, after how may vibrations are there in the same phase?

(a)

21

(b)

25

(c)

30

(d)

35

Find the period of a simple pendulum 1.20 m long _____________.

(a)

1.4 s

(b)

3.2 s

(c)

4.1 s

(d)

2.2 s

A pendulum 1.20 m long is observer to have 1 m Long is observed to have a period of 2.00 s at a certain location then the acceleration due to gravity is _______________.

(a)

9.71 m/s²

(b)

9.85 m/s²

(c)

9.79 m/s² 

(d)

10.1 m/s²

The three springs with force constant \({ k }_{ 1 }=8\frac { N }{ m } ,{ k }_{ 2 }=10\frac { N }{ m } ,{ k }_{ 3 }=12\frac { N }{ m } \), are connected in series to a mass of 0.500. The mass is then pulled to the right and released. Then the period of the motion is ________________.

(a)

2s

(b)

2.2s

(c)

2.5s

(d)

3.1s