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