spring-mass system?

Question

3 kg object attached to a horizontal spring oscillates with A=10cm and f = 2Hz. find...
a) force constant of the spring
b) period
c) max speed
d) max acceleration

Answer 1

a) w = sqrt(k/m) where w is in rad/s. Therefore force constant k = 473 N/m
b) period = T = 1/f = 0.5 sec

X = Asin(wt) = A*sin(sqrt(k/m)*t) If you differentiate that, you get speed, differentiate again and you get acceleration.

c) v = A*sqrt(k/m)*cos(sqrt(k/m)*t) The max speed would be at the time that the cos evaluates to equal 1.
d) a = -A*(k/m)*sin(sqrt(k/m)*t) Max when sin = 1

Note: if you leave A in cm, your speed and acceleration will be in cm.

Check out http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html#c1 and all the links it gives you.

Answer 2

the flexibility potential of the spring is given via formulation: ability potential = a million/2 (spring consistent x extension squared). Calculate the flexibility potential first. 0.5 this value to get the cost of the kinetic potential Use Kinetic potential = a million/2 (mass x velocity squared)