How Long Until Mass Reaches 0.05m in Oscillatory Motion?

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Homework Help Overview

The problem involves a mass-spring system where a mass of 0.2 kg is suspended from a spring, stretching it by 0.04 m. The mass is then pulled down an additional 0.1 m and released. The question seeks to determine the time at which the position of the mass equals 0.05 m during its oscillatory motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating the spring constant and angular frequency based on the initial conditions. There are attempts to express the position of the mass in terms of time using cosine functions. Some participants question the clarity of the provided frequency and period without units.

Discussion Status

The discussion includes various approaches to solving the problem, with some participants providing guidance on how to set up the equation for position over time. Multiple interpretations of the problem are being explored, particularly regarding the mathematical representation of the motion.

Contextual Notes

There is a lack of explicit units for the period and frequency mentioned, which some participants note as a point of confusion. The problem involves several parts, and the original poster indicates they have completed earlier sections but are now focused on the specific timing question.

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ok here's the problem:

When a mass of 0.2kg is suspended from a spring, it stretches 0.04m. The mass is pulled down an additional distance 0.1m from its equilibrium position and released.

Question:

how long after being released is the posiiton of the mass equal to 0.05m
 
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Use the first statement to find the spring constant. Divide it by the mass and find its square root. That gives you the angular frequency and you should be able to take it from there.
 
Last edited:
Tide said:
Use the first statement to find the spring constant. Divide it by the mass and find its square root. That give you the angular frequency and you should be able to take it from there.


i've found all of those. there are several parts to this question. I've done them up to this question which I'm stuck on.

the constant k=49
period T= .4
frequency f= 2.5
 
If you have those then you should know that, taking x to be the distance from the equilibrium position, positive above, negative below, x= -0.1 cos(2pi t/.4). To answer the question "how long after being released is the posiiton of the mass equal to 0.05m", set x= 0.05 and solve for t.

By the way, do you understand that saying "period T= .4 frequency f= 2.5" doesn't mean anything unless you give the units?
 

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