phy1ass1
Post on 05-Apr-2018
214 Views
Preview:
TRANSCRIPT
-
7/31/2019 phy1ass1
1/2
Physics 1 (Assignment 1)
1 A weight suspended from a spring extends it by x = 9.8cm. What will be theoscillation period of the weight when it is pushed gently in the vertical direction? The
logarithmic decrement is equal to = 3.1[ans: T = 0.70sec]
2 Find the quality factor of an oscillator whose displacement amplitude decreases by
a factor = 2.0 every n = 110 oscillations.[ans: Q = 500]
3 A particle is displaced from the equilibrium position by a distance l = 1.0cm andthen left alone. What is the distance that the particle covers till its oscillations die down,
if the logarithmic decrement is equal to = 0.020?[ans: s = 2m nearly]
4 Find the quality factor of a simple pendulum of length l = 50 cm if during the time
interval = 5.2minutes its total mechanical energy decreases by a factor = 4.0104.[ans: Q = 1.3
102]
5 A spring mass system has an undamped time period T0 = 2seconds. It is thensubject to critical damping. The mass is pulled to one side and then released from rest
at t= 0. Find the time in seconds, (0 < < ), at which the damping force exactlybalances the spring force.
[ans:= 1second]
6 A particle of mass m can perform undamped harmonic oscillations about a point
x = 0, with a natural frequency 0. At the moment t = 0, when the particle is inequilibrium, a force Fx = F0cost along the x axis is applied to it. Find the law offorced oscillations x(t) of the particle.
[ans: x =
F0
m
2 20(cos0t cost)]
7 A particle of mass m can perform undamped harmonic oscillations due to an elastic
restoring force with a spring constant k. When the particle is in equilibrium, a constant
force F is applied to it for seconds. Find the amplitude of oscillation of the particleafter the force ceases.
[ans: a = (2F
k) | sin(0/2) |, where 0 =
k
m]
1
-
7/31/2019 phy1ass1
2/2
8 A forced harmonic oscillator has equal displacement amplitude at the frequencies
1 = 400s1
and 2 = 600s1
. Find the resonance frequency at which the displacementamplitude is maximum.
[ans: res = 5.1102s1]
9 The velocity amplitude of a particle is equal to half its maximum value at frequen-
cies 1and 2 of an external harmonic force. Find:(a) The frequency corresponding to the velocity resonance;
(b) The damping coefficient and the damped oscillation frequency of the parti-cle.
[ans: (a) 0 =12; (b) =| 12 | /2
3, =
12 [(12)2/12]]
10 A mass m = 50g is suspended by a massless spring with a spring constant =
20.0N/m. The mass performs steady state vertical oscillations of amplitude a = 1.3cmdue to an external harmonic force of frequency = 25.0s1. The displacement lagsbehind the force by an angle = (3/4). Find:
(a) the quality factor of the given oscillator;
(b) the work performed by the external force in one oscillation.
[ans: (a) Q = 2.2 (b) W= 6mJ]
11 A mass m suspended by a massless spring performs vertical oscillations with a
damping coefficient . Its natural frequency is 0. The mass performs vertical os-cillations in the steady state due to an external vertical harmonic force varying as
F= F0cost. Find:(a) the mean power < P> developed by the force in one cycle;(b) the frequency at which < P > is maximum and the value of its maximum
average power < P>max.
[ans: (a) < P>=F20
2/m
(20 2)2 + 422; (b) = 0, < P>max=
F204m
]
2
top related