Ask Question, Ask an Expert


Ask Physics Expert

problem 1:

a) A simple harmonic oscillator has amplitude of 0.17 m and a period of 0.84 s. Find out the frequency and the angular frequency of the motion. prepare down expressions for the time dependence of displacement, velocity and acceleration. What are the maximum values of the velocity and acceleration?

b) Assume that a spring-mass system has k = 18 Nm-1 and m = 0.71 kg. The system is oscillating with amplitude of 54 mm.

i) Find out the angular frequency of oscillation.
ii) Obtain an expression for the velocity v of the block as a function of displacement, x and compute v at x = 34 mm
iii) Obtain an expression for the mass’s distance |x| from the equilibrium position as a function of the velocity v and compute | x | when v = 0.18 ms−1
iv) Compute the energy of the spring-mass system.

problem 2:

a) Establish the equation of motion of a damped oscillator. Show that for a weakly damped oscillator, displacement is given by:

x(t) = ao exp (-bt) sinωdt

As well obtain the expression for the time period of oscillation.

b) The weight on a vertical spring undergoes forced vibrations according to the given equation:

d2x/dt2 + 4x = 8 sin ωt

Where x is the displacement from the equilibrium position and ω > 0 is a constant. If at t = 0, x = 0 and v (= dx/dt) = 0; Compute

i) x as a function of t, and
ii) The period of the external force for which resonance takes place.

problem 3:

a) A sinusoidal wave is illustrated by:

y (x, t) = 2.0 sin (2.11 x – 3.62 t)

Where x is the position all along the wave propagation. Find out the amplitude, wave number, wavelength, frequency and velocity of the wave.

b) The linear density of a vibrating string is 1.3 × 10−4 kg m−1. A transverse wave is propagating on the string and is illustrated by the equation:

y (x, t) = 0.021 sin (x − 30t)

Where x and y are in meters and t is in seconds. Compute the tension in the string.

c) A transverse wave of amplitude 0.01 m is produced at one end (x = 0) of a long horizontal string by a turning fork of frequency 500 Hz. At a given instant of time, the displacement of the particle at x = 0.1 m is − 0.005 m and that of the particle at x = 0.2 m is 0.005 m. Compute the wavelength and the wave velocity.

problem 4:

a) A travelling wave is illustrated by the equation:

y = exp (− az2 – bt2 − 2 √ab zt)
Compute the wave velocity and sketch the waveform at t = 0 and t = 3s. Take a = 144 cm−2 and b = 9 s−1.

b) A stretched string of mass 20 g vibrates with a frequency of 30 Hz in its basic mode and the supports are 40 cm apart. The amplitude of vibrations at antinode is 4 cm. Compute the velocity of propagation of the wave in the string and also the tension in it.

c) Consider two cylindrical pipes of equivalent length. One of such acts as a closed organ pipe and the other as open organ pipe. The frequency of the second harmonic in the closed pipe is 200 Hz higher than the first harmonic of the open pipe. Compute the fundamental frequency of the closed pipe.

Physics, Academics

  • Category:- Physics
  • Reference No.:- M92516
  • Price:- $70

Priced at Now at $70, Verified Solution

Have any Question? 

Related Questions in Physics

Students should submit the exam at the beginning of the

Students should submit the exam at the beginning of the class.The exam will be conducted according to the policies outlined in the Northeastern University honor code. It is expected that you will work independently and i ...

Global temperatures have been rising on average for more

Global temperatures have been rising, on average, for more than a century, sparking concern that the polar ice will melt and sea levels will rise. With t in years since 1880, fitting functions to the data10 gives three m ...

Chicken eggs possess a hard porous shell of calcite mineral

Chicken eggs possess a hard, porous shell of calcite mineral. Cylindrical pores of 10micron diameter running through the 0.5mm thickness of the shell permit the exchange of gasses to the inner membrane and egg yolk. A ty ...

Investigate how fast sexual and asexual species evolve if

Investigate how fast sexual and asexual species evolve if they have a fitness function with interactions. For example, let the fitness be a sum of exclusive-ors of pairs of bits; compare the evolving fitnesses with those ...

An object with a mass of 3 kg falls freely from rest for 3

An object with a mass of 3 kg falls freely from rest for 3 seconds. Calculate the acceleration.

There is a three-phase ig of 110 v 60nbsphz 4 poles 1900

There is a three-phase IG of 110 V, 60 Hz, 4 poles, 1900 rpm, Y stator connection, and an equivalent circuit given as R 1 = 0.20 Ω, R 2  = 0.42 Ω, X 1  = 0.15 Ω, and X 2  = 0.43 Ω; R 2  and X 2  refer to the stator. The ...

A 15-kg projectile is fired from level ground the vertical

A 1.5-kg projectile is fired from level ground. The vertical component of the initial velocity is 65 m/s and the horizontal component is 29 m/s. Ignore air resistance and the curvature of the earth in this problem. How f ...

Explain alienation from species being what is so tragic

Explain alienation from species being. what is so tragic about this form of alienation according to Marx? Define the "fetishism of commodities", Start by using the original definition of "fetish", transition into the Mar ...

What is the error in the boltzmann approximation if the

What is the error in the Boltzmann approximation if the crystal size is not infinite but contains 10 2 , 10 3 , 10 4 , 10 5 , 10 6 , 10 9  atoms? This is a very real situation in submicron transistors In which an active ...

Starting with the einstein relationship derive the

Starting with the Einstein relationship, derive the Boltzmann relationship for the equilibrium electron concentration, N(x)-N(x 1 )exp{q[V(x)-V(x 1 ))/kT]. Is this result consistent with the fact negatively charged elect ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen