Ineed with parts 3, 6, and 7 you can ignore the graphing parts you!
a cart weighs 8 pounds is attached to the wall by a spring with spring constant k = 2 lb/ft. the cart is pulled 1 ft in the direction away from the wall, and released with the given initial velocity 2 ft/sec.
assuming there's no friction/air resistance (no dumping) , write down the ode
solve the ode and graph it in desmos
what are its natural frequency, period and amplitude?
case a: assuming friction/air resistance (dumping) exists and it's measured as 10 lb/ft proportional to the cart's speed.
write down ode
solve the ode and graph it in desmos
case b: assuming friction/air resistance (dumping) exists and it's measured as 8 lb/ft proportional to the cart's speed.
write down ode
solve the ode and graph it in desmos
case c: assuming friction/air resistance (dumping) exists and it's measured as 2 lb/ft proportional to the cart's speed.
write down ode
solve the ode and graph it in desmos
case d: back to the no dumping case, however a periodic external force latex: f\left(t\right)=2\: \sin\left(4t\right) f(t)=2sin⁡(4t)is applied to the cart
write down the ode
solve the ode