PLEASE HELP! I\'ve been trying but for some reason whatever I plug iin something

Question

PLEASE HELP! I've been trying but for some reason whatever I plug iin something is wrong! Is my calculator supposed to be in degrees mode?

Your answer is partially correct. Try again. A simple harmonic oscillator consists of a block of mass 4.50 kg attached to a spring of spring constant 260 N/m, when t = 0.830 s, the position and velocity of the block are x0.194 m and v 3.210 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? (a) Number 46472 Unii (b) Number 464 Units m Units m/s (c) Number 3.53 () Number 2.53

Explanation / Answer

here,

mass , m = 4.5 kg

spring constant , K = 260 N/M

w be the angular frequency

w = sqrt(k/m)

w = sqrt(260/4.5)

w = 7.6 rad/s

for simple harmonic motion,

the distance, y = A * sin(w*t + theta)

velocity , v = A* w * cos(w*t + theta)

at t = 0.83, y = 0.194 and v = 3.21 m/s

0.194 = A * sin(7.6 * 0.83 + theta)

3.21 = A *7.6 * cos(7.6 * 0.83 + theta)

solving for theta nad A

A = 0.46 m , theta = 18.43 degree

(a)

the amplitude of the oscillation is 0.46 m

(b)

y = 0.46 * sin(7.6 * t +18.42)

at t= 0

y = 0.46 * sin(18.42)

y = 0.15 m

the position at t=0 is x = 0.15 m

(c)

v = 0.46* 7.6 * cos(7.6 * t +18.42)

at t= 0

v = 0.46 * 7.6 * 0.95

v = 3.32 m/s

the velocity of block at t= 0 is 3.32 m/s

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