Aspring mass system is characterized by k=16Nm/sec and m=1.0kg .the system is oscillating with an amplitude of 0.20m then i) calculate the angular velocity of oscillation.ii)obtain an expression for the velocity of the block as a function of displacement and calculate its value at X=0.1m .iii)calculate energy of the spring mass system

1
by sweta1234
A spring mass system is characterized by k=16Nm-1 and m=1 kg. The system is oscillating with an amplitude of 0.20 m.

Answers

2015-09-10T21:03:25+05:30

This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
A spring mass system oscillates in a simple harmonic motion with an angular speed  ω.  The restoration force F due to the spring on the mass m is given by:

F = m d²x/dt² = - k x
d²x /dt² = - (k/m) x    = - ω² x
ω = √(k/m)  = √16/1 = 4 rad/sec
as k = 16 N m/sec  and  m = 1.0 kg

Amplitude = A = 0.20 meters
============
The displacement x from its mean position at any point of time t of the mass m can be given as:
x = A Sin (ω t)  = 0.20 Sin 4 t

velocity instantaneous  of the mass = v = dx/dt =
v = A ω Cos ωt        obtained by differentiating x wrt t.
= ω √[A² - x²]

So  v = 4 * √[ 0.2² - 0.1²]  = 0.4 * √3 m/sec
=======================

Energy of the spring mass system is the total potential energy when the displacement is maximum ie., displacement = amplitude  or  the total KE when the displacement is 0.

Total energy  =  1/2 k A²  = 1/2 * 16 * 0.2² = 0.32 Joules.

we can also calculate this as follows:
The velocity of the mass when x = 0 is:  v = ω A
So  total energy = 1/2 * m * v² = 1/2 * 1 * (4 * 0.2)² = 0.32 Joules

click on thanks button above