Question

z waqod A 2- kg block attached to a spring undergoes simple harmonic motion described by = (30 cm) cos[(6.28 rad/s)t + /4]. Determine (a) the amplitude, (b) the spring constant, (c) the frequency, (d) the maximum speed of the block, (e) maximum acceleration of the block, and (e) the total energy of the spring-block.

Answer 1

Q2 compare the equation x = A cos ( wt + theta) where theta is initial phase

A= 30cm

wt= 6.28t

w= 6.28 = (k/m)^1/2

Square both sides

39. 4384 = k/m

k= 39.4384 x2 = 78.876N/m

Frequency

w= 2x pi x frequency

Frequency = 6.28/2×3.14 = 1Hz

Maximum speed = Aw= 0.3 x 6.28= 1.884m/S

Maximum acceleration = Aw^2= 0.3 x 6.28 x 6.28 = 11.83 m/s^2

Total energy = 1/2kA^2= 0.5 x 78.876 x 0.3 x0.3= 3.549J

Q 3

1/2 kA^2= 2

1/2 × k x 0.2 x0.2= 2

K= 100N/m

T =1.5s

T = 2x pi ( m/k)^1/2

1.5 = 2x 3.14 x ( m/ 100)^1/2

m= 5.7kg