Frequency to Angular Frequency

Q. An object of mass $0.5\text{kg}$ is executing simple harmonic motion. Its amplitude is $5\text{cm}$ and time period $\left(T\right)$ is $0.2\text{s}.$ What will be the potential energy of the object at an instant $t=\frac{T}{4}\text{s}$ starting from the mean position . Assume that the initial phase of the oscillation is zero.

1. $0.62\text{J}$
2. $6.2\times {10}^{-3}\text{J}$
3. $1.2\times {10}^3\text{J}$
4. $6.2\times {10}^3\text{J}$

Q. A mass of $2.0\text{kg}$ is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is $200\text{N/m}$. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (Take $g=10{\text{m/s}}^2$)?

1. $10\text{cm}$
2. any value less than $12\text{cm}$
3. $4\text{cm}$
4. $8\text{cm}$

Q.

A transverse wave propagating on a stretched string of linear density $3\times {10}^{-4}kg{m}^{-4}$ is represented by the equation, $y=\left(0.02\right)\sin \left[1.5x+60t\right]$, where, $x$ is in meter and $t$ is in second. The tension in the string (in newton) is

1. $0.48$

2. $0.24$

3. $1.20$

4. $1.80$

Q. Find the natural frequency of oscillation of the system shown in the figure. Pulleys are massless and frictionless. Spring and strings are also massless.

1. $\frac{\pi }{2}\text{Hz}$
2. $\sqrt{\pi }\text{Hz}$
3. $\frac{10}{\sqrt{\pi }}\text{Hz}$
4. $\pi \text{Hz}$

Q. Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed of $1.0m{s}^{-1}$ and the man behind walks at a speed of $2.0m{s}^{-1}$. A third man is standing at a height $12m$ above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency $1430Hz$. The speed of sound in air is $330m{s}^{-1}$. At the instant, when the moving men are $10m$ apart, the stationary man is equidistant from them. The frequency of beats in $Hz$. heard by the stationary man at this instant, is ______

Q. A particle of mass M is suspended by two ideal strings as shown in the figure. Now, mass M is given a small displacement perpendicular to the plane of triangle formed. Choose the correct statement(s).

1. The period of oscillation of the system is $2\pi \sqrt{\frac{3\sqrt{3}l}{g}}$
2. The period of oscillation of the system is $2\pi \sqrt{\frac{3l}{g}}$
3. The period of oscillation of the system is independent of M.
4. If the distance between the suspension points was kept constant and the lengths of the strings were quadrupled, then the period of the system will double.

Q. What is the relation between frequency f of and oscillation and its angular frequency $\omega$

1. 2 $\pi \omega$ = f
2. $\omega$ = 2 $\pi$f

Q. A $1\text{kg}$ block is executing simple harmonic motion of amplitude $0.1\text{m}$ on a smooth horizontal surface under the restoring force of a spring of spring constant $100\text{N/m}$. A block of mass $3\text{kg}$ is gently placed on it at the instant it passes through the mean position. Assuming that the blocks move together, then

1. Amplitude of the motion becomes $5\text{cm}$
2. The oscillation frequency becomes $\frac{5}{2\pi }\text{Hz}$
3. Amplitude of the motion becomes $10\text{cm}$
4. The oscillation frequency becomes $\frac{5}{\pi }\text{Hz}$

Q. What is the relation between frequency f of and oscillation and its angular frequency $\omega$

1. $\omega$ = 2 $\pi$f
2. 2 $\pi \omega$ = f

Q. A light wooden rod fixed at one end is kept horizontal. A load of $0.4\text{kg}$ tied to the free end of the rod causes that end to be depressed by $2.8\text{cm}$ . If this load is set into up and down vibrations, with what frequency(in $\text{Hz}$) will it oscillate?

Q. A block of mass \(M\) is attached with tow springs as shown and oscillates. Surface is smooth. If the maximum velocity of blcok is \(v_0\) durign the motion, then amplitude of oscillation is

Q. Which of the following has the highest Potential energy?

1. 10 kg stone at a height of 20 m
2. 100 kg stone at a height of 2 m
3. 40 kg stone at a height of 5 m
4. 30 kg stone at a height of 7 m

Q. An elevator car whose floor-to-ceiling distance is equal to 2.7m starts ascending with a constant acceleration $1.2m/s^2;2.0s$ after the start a bolt begins falling from the ceiling of the car. Find the displacement covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.

1. 0.7 m
2. 1.7 m
3. 2.7 m
4. 3.7 m

Q.
A block of mass $m=2\text{kg}$ is placed on an inclined smooth surface of inclination $\theta ={60}^{\circ }$. One end of a massless spring of relaxed length $50\text{cm}$ and spring constant $k$ is fixed on top of a plane. A block is attached with another end of spring extends by $2.5\text{cm}$. The mass is displaced slightly and released, the time period of resulting oscillation will be,

1. $1.17\text{sec}$
2. $0.17\text{sec}$
3. $0.34\text{sec}$
4. $1.54\text{sec}$

Q.

Inside a physics lab: (vibrating tuning fork does SHM)

Teacher: this experiment is about finding the frequency of oscillation of different tuning forks.

You hit it against something and take it close to this device [pointing at the device] which measures the frequency. The oscillation of a tuning fork is simple harmonic.

Student X hits a thick tuning fork lightly and finds out its frequency as f. student x then hits a thin one lightly and finds its frequency to be f'. student x thinks if he hit the thick one hard enough its frequency might come out to be f'. The student tries this.

1. He/she finds out that this is possible

2. The frequencies never become same

3. The frequency does become equal/or close on hitting a bit more harder

4. He/she finds out that it is not possible.

Q. A rod of mass $M$ and length $2L$ is supended at its middle by a wire. It exhibits torsional oscillations. If two masses each of $m$ are attached at distance $\frac{L}{2}$ from its centre on both sides, it reduces the oscillation frequency by $20\%$. The value of ratio $\frac{m}{M}$ is close to

1. $0.77$
2. $0.17$
3. $0.57$
4. $0.37$

Q. Two pendulums $X$ and $Y$ of time periods $4s$ and $4.2s$ are made to vibrate simultaneously. They are initially in same phase. After how many vibrations of $X,$ they will be in the same phase again?

1. $30$
2. $25$
3. $21$
4. $26$

Q. The frequency of oscillation of a mass $m$ suspended by a spring is $\nu$. If the length of the spring is cut to one third then the same mass will oscillate with frequency

1. $\sqrt{2}\nu$
2. $\sqrt{3}\nu$
3. $\sqrt{5}\nu$
4. $\sqrt{6}\nu$

Q. Physics is sometimes referred to as exact science. Because.

1. Due important is given for the measurement of quantities
2. Physics interacts with almost all the sciences
3. It involves philosophy
4. Physics is related more closely to mathematics than any other science

Q. The total weight of a piece of wood is 6 kg. In the floating state in water, its $\frac{1}{3}$ part remains inside the water. On this floating solid, what maximum weight is to be put such that whole of the piece of wood is drowned in the water?

1. 12 kg
2. 10 kg
3. 14 kg
4. 15 kg

Q. The potential energy of a body of mass $0\cdot 5kg$ increases by $100J$ when it is taken to the top of a tower from ground. If force of gravity on $1kg$ is $10N$, what is the height of the tower?

Q. Physics involves the study of the

1. plants
2. humans
3. nature and natural phenomena
4. birds and animals

Q. A spring mass system is shown in figure, spring is initially unstretched. A man starts pulling the block with constant force $F$. Find
(a) The amplitude and time period of motion of the block
(b) The kinetic energy of the block at mean position
(c) The energy stored in the spring when the block passes through the mean position.

Q. Amplitude of a mass spring system, which is executing simple harmonic motion decreases with time. If mass $=500\text{g}$, damping constant $=20\text{g/s}$ then how much time is required for the amplitude of the system to drop to half of its initial value?
$(ln2=0.693)$

1. $15.01\text{s}$
2. $17.32\text{s}$
3. $0.034\text{s}$
4. $34.65\text{s}$

Q. Angular frequency is defined as the rate of change of angular displacement.

1. True
2. False

Q. An elevator of mass 400 kg is moving upwards and the tension in the supporting cable is 40, 000 N. Find the upward acceleration . How far does it rise in a time of 10 s starting from rest(g=9.8 m/$s^2$)

Q.

A horizontal spring is connected to a mass M. It executes simple harmonic motion. When the mass M passes through its mean position, an object of mass m is put on it and the two move together. The ratio of frequencies before and after will be-

1. ${\left(1+\frac{m}{M}\right)}^{1/2}$
2. $\left(1+\frac{m}{M}\right)$
3. ${\left(\frac{M}{M+m}\right)}^{1/2}$
4. $\left(\frac{M}{M+m}\right)$

Q. Calculate power generated by tension in the string in first $2$ seconds of motion.

1. $250$ W
2. $500$ W
3. $750$ W
4. $1000$ W

Q. What is the relation between frequency f of and oscillation and its angular frequency $\omega$

1. $\omega$ = 2 $\pi$f
2. 2 $\pi \omega$ = f

Q. A person P is 600 m away from the station when train is approaching station with 72 km/h, it blows a whistle of frequency 800 Hz when 800 m away from the station. Find the frequency heard by the person. speed of sound = $340m{s}^{-1}$

1. 839.5 Hz
2. 829.5 Hz
3. 800 Hz
4. 843.5 Hz