Question

A cart of mass 300 g is placed on a frictionless horizontal air track. A spring having a spring constant of 9.0 N/m is attached between the cart and the left end of the track. The cart is displaced 3.8 cm from its equilibrium position. (a) Find the period at which it oscillates. Correct: Your answer is correct. s (b) Find its maximum speed. Incorrect: Your answer is incorrect. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s (c) Find its speed when it is located 2.0 cm from its equilibrium position. m/s

Answer 1

Step-by-step explanation:

the angular frequency ω of the pendulum is given by the formula

ω =
`\sqrt{(k)/(m) }` , k is spring constant , m is mass attached .

=
`\sqrt{(9)/(.3) }`

= 5.48 rad /s

time period = 2π / ω

= 2 x 3.14 / 5.48

= 1.146 s

b ) formula for speed

v = ω
`√((a^2-\ x^2))` , a is amplitude , x is displacement from equilibrium point.

for maximum speed x = 0

max speed = ωa

= 5.48 x 3.8 x 10⁻² ( initial displacement becomes amplitude that is 3.8 cm )

= .208 m /s

20.8 cm / s

c )

when x = .02 m , velocity = ?

v = ω
`√((a^2-\ x^2))`

= 5.48
`√((.038^2-\ .02^2))`

= 5.48 x .0323109

= .177 m /s

17.7 cm /s .