A particle with a mass of 3 . 00 × 10 - 20 kg is oscillating with simple harmonic motion with a period of 2 . 00 × 10 - 5 s and a maximum speed of 1 . 00 × 10 3 ms - 1 . Calculate (a) the angular frequency and (b) the maximum displacement of the particle.

Given: Mass of particle, m = 3 × 10 - 23 kg . Time period, T = 2 × 10 - 5 s . Maximum speed, v max = 10 3 ms - 1 . (a) Angular frequency of the oscillator will be, ω = 2 π T = 3 . 142 × 10 5 Hz . (b) Applying the conservation of energy we get, 1 2 m ω 2 A 2 = 1 2 m v max 2 where, the amplitude is given by, A = v max ω = 3 . 18 × 10 - 3 m .

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An object undergoing simple harmonic motion takes $0.25 s$ to travel from one point of zero velocity to the next such point. The distance between those points is $32 cm$ . Calculate the (a) period, (b) frequency and (c) amplitude of the motion.

Important Questions on Oscillations

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Principles Of Physics International Student Version>Chapter 15 - Oscillations>Problems>Q 1

In the figure, two identical springs of spring constant $7580 N m^{- 1}$ are attached to a block of mass $0.270 kg$ . What is the frequency of oscillation on the frictionless floor?

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Principles Of Physics International Student Version>Chapter 15 - Oscillations>Problems>Q 22

An automobile can be considered to be mounted on four identical spring as far as vertical oscillation are concerned. The springs of a certain car are adjusted so that the oscillations have a frequency of $3.00 Hz$ .

(a) What is the spring constant of each spring if the mass of the car is $2110 kg$ and the mass is evenly distributed over the spring?

(b) What will be the oscillation frequency if five passenger averaging $85.0 kg$ each ride in the car with an even distribution of mass?

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Principles Of Physics International Student Version>Chapter 15 - Oscillations>Problems>Q 31

If a stick of length $L = 1.65 m$ oscillates as a physical pendulum.

(a) What value of the distance $x$ between the stick's centre of mass and its pivot $O$ gives the least period?

(b) What is that least period ?

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Principles Of Physics International Student Version>Chapter 15 - Oscillations>Problems>Q 52

If the phase angle for a block-spring system in S.H.M. is

π / 8 rad

and the block's position is given by

x = x_{m} \cos (ω t + ϕ)

, what is the ratio of the kinetic energy to the potential energy at time

t = 0

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Principles Of Physics International Student Version>Chapter 15 - Oscillations>Problems>Q 53

An oscillator consists of a block attached to a spring

(k = 425 N m^{- 1})

. At some time

t

, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are

x = 0.100 m, v = - 13.6 m s^{- 1}

and

a = - 123 m s^{- 2}

. Calculate (a) the frequency of oscillation, (b) the mass of the block, and (c) the amplitude of the motion.

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Principles Of Physics International Student Version>Chapter 15 - Oscillations>Problems>Q 54

An oscillating block-spring system takes

0.25 s

to begin repeating its motion. Find (a) period, (b) the frequency in hertz, and (c) the angular frequency in radians per second.

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Principles Of Physics International Student Version>Chapter 15 - Oscillations>Problems>Q 55

A performer seated on a trapeze is swinging back and forth with a period of

8.85 s

. If she stands up, thus raising the center of mass of the system trapeze + performer system by

40.0 cm

. What will be the new period of the system? Treat trapeze + performer as a simple pendulum.

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Principles Of Physics International Student Version>Chapter 15 - Oscillations>Problems>Q 56

A particle with a mass of

3.00 \times 10^{- 20} kg

is oscillating with simple harmonic motion with a period of

2.00 \times 10^{- 5} s

and a maximum speed of

1.00 \times 10^{3} {ms}^{- 1}

. Calculate (a) the angular frequency and (b) the maximum displacement of the particle.

An object undergoing simple harmonic motion takes 0.25 s to travel from one point of zero velocity to the next such point. The distance between those points is 32 cm. Calculate the (a) period, (b) frequency and (c) amplitude of the motion.

Important Questions on Oscillations

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An object undergoing simple harmonic motion takes $0.25 s$ to travel from one point of zero velocity to the next such point. The distance between those points is $32 cm$ . Calculate the (a) period, (b) frequency and (c) amplitude of the motion.