Solving a Mass Supported by a Spring: Explaining Assumptions

[laura11]

plllease help!

A mass is supported by a spring so that it is at rest 0.5 m above a tabletop. The mass is pulled down 0.4 m and released at time t = 0, creating a periodic up and down motion that can be modeled using a trigonometric function. It takes 1.2 seconds to return to the lowest position each time.

Write an equation for the function in part a). [4]


What assumption(s) must be made for this function to be valid? Explain.

The Attempt at a Solution

i have no idea

 

[Office_Shredder]

What is the function in part (a) supposed to be? The position of the mass?

What kind of function do you think it's going to be?

 

[laura11]

sin?

 

[jgens]

Why don't you try drawing a picture of what the question describes along with a position v. time graph? This can help you figure out how to create a satisfactory function.

 

[laura11]

my problem is that i don't know how to find proper phase shift, period etc

i understand what's happening and everything
i came up with an equation but it just wasnt right

 

[jgens]

Did you draw the position v. time graph? If so, describe what you drew here and your reason for doing so.

 

[HallsofIvy]

No one can help you if you won't tell us what you are trying to do! You say you are trying to find a function, but a function to describe what? Please answer Office_Shredders first questions: "What is the function in part (a) supposed to be? The position of the mass?"

 

[laura11]

no but i don't think that will help because the problem is figuring out what the function is

 

[jgens]

no but i don't think that will help because the problem is figuring out what the function is

You do realize that a function and it's graph are related, right? Given the position v. time graph, it's extremely easy to deduce what the proper function should be in this case.

 

[laura11]

oook ill do it

 

[Rasalhague]

Often when people are familiar with questions like this, they can forget how many unstated assumptions there are, and how confusing it can be for someone who hasn't seen so many of them. This question is asking for an equation that will tell you the height of the mass if you know its time: an equation for height as a function of time. So if we call height h and time t, the equation will have h on one side and something involving t on the other. You guessed that sine might have something to do with it. That's a good start. It would be nice if it was just sin(t), but, as you know, that doesn't quite give the answer you're looking for. But it's not far off... The graph is the right shape at least, and its amplitude its right. Think what changes would you need to make to sin(t) to make its graph like the graph you want.

If you don't have a calculator or computer program to plot functions, there are lots online, such as this or this. If you're stuck for ideas, play around with that equation, see what happens when you change things. Think what values of t and h you already know: when t = 0, h = ..., when t = 1.2, h = ..., and think how you can use those changes to make the equation fit.

If you need some background on graphing trigonometric functions, what they look like and why, and how stuff like phase and amplitude are represented in their equations, the Khan Acedemy has some good videos on this subject, especially these in the Trigonometry playlist:

Graph of the sine function
Graphs of trig functions
Graphing trig functions
More trig graphs
Determining the equation of a trigonometric function

 

[laura11]

thanks!