Question

[Q2-Home/Lab ⋆⋆⋆] We attach a known weight (~100 gr) from the spring that is provided in the lab. By pulling down the spring by no more a couple of cm put it in oscillating mode. This experiment is described here [the screencast can be played in the classroom in mute as long as you keep an eye to spot the information you need] Get the data from the experiment here. Q2a) Calculate the theoretical period and compare it to the observed period (use the first ~100 time-steps) Q2b) Calculate the theoretical maximum speed and compare it to the observed maximum speed (use the first ~100 time-steps) Q2c) Calculate the theoretical maximum acceleration and compare it to the observed maximum acceleration (use the first ~100 time-steps)

Answer 1

Since no data is provided, the general formulas and their derivations are given here.

m = mass attached to spring(kg); a = acceleration (m/s2); x = distance of mass from its equilibrium positon(m); k = spring constant(N/m);

Q2a) Time period, T

starting with Hooke's law, F = ma

=> m a = -k x

=> m a = -k x

=> a = (-k x)/m

using the condition for a simple harmonic motion,

where, =>

=>

THEREFORE,

Q2b) Velocity, V

using conservation of energy,

we get,

Q2c) Acceleration, a

from hooke's law,

ma = -kx

=>