Solving 2 Problems: Vertical Displacement & Mass on Spring

[subwaybusker]

I have two problems:

Homework Statement

I am given the positions and velocities of a mass on a spring at two times, which is four equations. I need to find the position and velocity of the mass at t=1s.

Homework Equations

0.35=-A$$\omega$$sin$$\phi$$
0.1=Acos$$\phi$$

-0.2=-A$$\omega$$sin($$\omega$$t$$\phi$$)
0.17=Acos($$\omega$$t$$\phi$$)

The Attempt at a Solution

I tried to divide the top two and the bottom two equations such that i got tan phi and tan omega t + phi, but after that i don't know how to manipulate the equations. i tried the tan identity but i couldn't do anything.

then i tried using 1/2*kx^2=1/2*mv^2 to get $$\omega$$ but the $$\omega$$ for the two times were different..

Second question:

poor diagram, please excuse me

wall-spring-mass-spring-wall

the two springs are of equal length and have equal k constant. I need to prove that when the mass is displaced VERTICALLY it does not have simple harmonic motion, assuming the vertical displacement is very small compared to the length of the spring.

Attempted Solution:

I drew a picture of the mass being displaced downwards and i got y=Lsintheta, but i know i am supposed to prove that the differential equation is not linear, so y (vertical displacement)ends up on the right of the Diff Eqn with a power or something. The Lsintheta isn't helped me, cause from what I have I can't see why y isn't linear.

 

[Andrew Mason]

Check the question. The general solution to the differential equation:

d^2x/dt^2 = kx/m

is

x = Asin (wt + phi ) where w^2 = km

AM

PS for some reason Latex does not appear to be working

 

[baba89]

I would approach these two problems by first understanding the underlying principles and equations involved. For the first problem, it seems like you are given the equations for simple harmonic motion of a mass on a spring, and you need to solve for the position and velocity at a specific time. I would start by reviewing the equations for simple harmonic motion and understanding how they relate to the given equations. From there, I would use algebraic manipulation and possibly substitution to solve for the position and velocity at the given time.

For the second problem, it seems like you are trying to prove that the vertical displacement of a mass on two equal springs does not exhibit simple harmonic motion. To do this, I would start by reviewing the definition of simple harmonic motion and the conditions that must be met for it to occur. From there, I would analyze the given system and determine if it meets those conditions. If it does not, I would then use mathematical analysis to show how the system does not follow the principles of simple harmonic motion. This could involve using the equations for simple harmonic motion and showing how they do not apply to this system, or using differential equations to show the non-linearity of the system.