What is the velocity of a block in SHM involving a spring after a given time?

  • Thread starter Thread starter Mdhiggenz
  • Start date Start date
  • Tags Tags
    Shm Spring
Click For Summary

Homework Help Overview

The problem involves a block executing simple harmonic motion (SHM) attached to a spring, with specific parameters provided, including mass, spring constant, and initial displacement. The objective is to determine the block's velocity at a given time after it is released from rest.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the appropriate equations for SHM, questioning the use of sine versus cosine functions based on the initial conditions of the motion. There is confusion regarding the correct form of the velocity equation and how to incorporate the amplitude into calculations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the SHM equations and clarifying the initial conditions. Some guidance has been offered regarding the choice of equations based on the starting position of the block.

Contextual Notes

There is a noted assumption that the block is released from maximum displacement, which affects the choice of trigonometric functions in the equations used. Participants are also grappling with the implications of the initial conditions on their calculations.

Mdhiggenz
Messages
324
Reaction score
1

Homework Statement


A 1.6-kg block on a horizontal frictionless surface is attached to a spring whose force constant is 190 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the x-axis (horizontal). The velocity of the block at time t = 0.40 s is closest to:



Homework Equations





The Attempt at a Solution



ω=√k/m=190/1.6=118.75 rad/s

v=-Aωcos(ωt)

=-0.080*(10.90)cos(10.90*.40)=.30m/s

However the answer is .8m/s

Am I missing a step?

Thank you
 
Physics news on Phys.org
You are using x = Asin(ωt). But that assumes that at t = 0 the mass is at x = 0.

(Pick a form that starts at maximum displacement.)
 
I don't quite understand what you are saying,

isnt the maximum displacement .080 which is the amplitude, I am not sure how to incorporate it.
 
Mdhiggenz said:
v=-Aωcos(ωt)
Where did this come from?

When they say "at time t = 0.40 s" they are measuring the time from the moment it was released, which is the point of maximum displacement.
 
Which means I use -waSin(wt)

since the graph of sin starts at zero?
 
Mdhiggenz said:
Which means I use -waSin(wt)

since the graph of sin starts at zero?
Yes.
 

Similar threads

Why is my thinking incorrect? -- Block and spring driven by a motor
  • · Replies 7 ·
Replies
7
Views
2K
Kinetic Energy from a Simple Harmonic motion and spring
  • · Replies 7 ·
Replies
7
Views
2K
How Long for a Block in SHM to Hit a Wall After Spring Snaps?
  • · Replies 6 ·
Replies
6
Views
2K
Finding time of how long the block travels (SHM)
  • · Replies 5 ·
Replies
5
Views
6K
Amplitude of a mass joined to a spring in the presence of an E-field
  • · Replies 5 ·
Replies
5
Views
2K
Finding Vmax of a Block in SHM: Mass, Spring Constant, and Distance
  • · Replies 5 ·
Replies
5
Views
4K
Block on Spring SHM, Finding angular frequency
  • · Replies 3 ·
Replies
3
Views
3K
Calculating Mass of a Block in SHM with Given Parameters
  • · Replies 14 ·
Replies
14
Views
8K
Finding time given positions in SHM
  • · Replies 5 ·
Replies
5
Views
16K
Simple Harmonic Oscillator: Mass Spring System
  • · Replies 2 ·
Replies
2
Views
2K