PHYSICS GENIUSES a little help please.it's about amplitude of motion, frequency and period of an object thnx!

Question

Ive been working on this physics problem... but i'm stuck.. i've been able to calculate only 2 of all (I wrote them on the line).. but the rest i don't know exactly.. on the second answer i get .6999 but i think it's wrong.. can anyone help me a bit?

The motion of an object is described by the equation below.
x = (0.70 m) cos("pi"t/4)

(a) Find the position of the object at
t = 0 ___.7______
and at
t = 0.60 s. ________

(b) Find the amplitude of the motion.
_____.7_____m
(c) Find the frequency of the motion.
__________Hz
(d) Find the period of the motion.
_________S

Answer 1

The position at t = 0.60 is (0.70) cos (π(0.60)/4)
= 0.624 m (3 d.p.).
I suspect you were in Degrees mode instead of Radians mode in your calculator when you computed the cos() function.

One period of the motion will occur when the argument of the cos() function changes by 2π, in other words when t/4 = 2 => t = 8. So the period is 8 seconds and hence the frequency is 1/8 Hz.

Answer 2

In general if you write your periodic function in the form: y = a cos b (x-h) +k |a| is the amplitude the period is 2π/b (h,k) is the displacement: h shifiting right or left, (phase shift.) k shifting the function up or down. Your functions: a. s = 3 cos 5t the amplitude is 3. the period is; 2π/b. Frequency is a relative measurement, (the number of waves this function has in a given period of time.) You have 5 waves in the same period of time that the cosine would have one, t=1 whatever units. (Generally we think of the frequency as 1/|b|.) If s is the speed then the velocity amplitude is the maximum value for s, (or the distance s is graphed above the t axis. In general |a| + k. Both of your functions k=0 so the velocity amplitude will equal |a|. b. s = 1/2 cos (πt - 8) amplitude = 1/2 period is: 2π/π=2 the frequency is 1/2.