Answer:
A. 2.249 hz
B. 0.45 s
C. 0.424 m/s
D. 66⁰
E. 6 m/s^2
Explanation:
<u>Step 1:</u> identify the given parameters
mass of the block (m)= 0.75kg
stiffness constant (k) = 150N/m
Amplitude (A) = 3cm = 0.03m
upward velocity (v) = 2cm/s
<u>Step 2:</u> calculate the natural frequency (F)by applying relevant formula in S.H.M
f = 2.249 hz
<u>Step 3:</u> calculate the period of the oscillation (T)
T = 0.45 s
<u>Step 4</u>: calculate the maximum velocity,
A is the amplitude of the oscilation
<u>Step 5:</u> calculate the phase angle, by applying equation in S.H.M
where X is the displacement; calculated below
Displacement = upward velocity X period of oscillation
X = (2cm/s) X (0.45 s)
X = 0.9 cm = 0.009m
where is omega; calculated below
Applying displacement equation in S.H.M
=72.5 -6.364
=66.1⁰
Phase angle, ≅66⁰
<u>Step 6:</u> calculate the maximum acceleration,
= 14.142 X 14.142 X 0.03
= 5.999
≅ 6