What is the phase of the SHM at that point

  • Thread starter Thread starter Voltrical
  • Start date Start date
  • Tags Tags
    Phase Point Shm
AI Thread Summary
The discussion revolves around a mass-spring system undergoing simple harmonic motion (SHM). For part a, the speed of the mass when the spring is compressed by 0.05 m is calculated to be 0.866 m/s. In part b, the phase of the SHM at that point is determined to be 120 degrees, which relates to the cosine function in the SHM equation. The participants clarify that the phase is derived from the relationship between amplitude and the position in the cycle. Understanding the phase angle is essential for analyzing the motion of the system.
Voltrical
Messages
11
Reaction score
0

Homework Statement



A mass is attached to a spring on a frictionless horizontal surface. The mass is pulled to stretch the spring by 0.1 m, & then gently released. A short time later, as the mass passes through the equilibrium position, its speed is 1 m/s.

Part a)

What is the speed of the mass at the point where the spring is compressed by 0.05 m?

Part b)

What is the phase of the SHM at that point, relative to a phase of zero at the time of release?

Homework Equations



The Attempt at a Solution



Part a)

A = 0.1 m
ωA =1 m/s
ω = 1 / 0.1 = 10 rad/s
y = 0.05 m
V = ω √ (A2 - y2)
= 10 * [ √ ( 0.01 - 0.0025 ) ]
= 0.866 m/s, this answer is correct because my teacher gave us the answer.

Part b)

Answer = 120°, how to get this answer?
 
Physics news on Phys.org
Hi Voltrical! :smile:
Voltrical said:
Part b)

Answer = 120°, how to get this answer?

shm is amplitude times cosωt …

so won't it have something to do with cos120° ? :wink:
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top