Answer:
0.67 s
Explanation:
This is a simple harmonic motion (SHM).
The displacement,
, of an SHM is given by

A is the amplitude and
is the angular frequency.
We could use a sine function, in which case we will include a phase angle, to indicate that the oscillation began from a non-equilibrium point. We are using the cosine function for this particular case because the oscillation began from an extreme end, which is one-quarter of a single oscillation, when measured from the equilibrium point. One-quarter of an oscillation corresponds to a phase angle of 90° or
radian.
From trigonometry,
if A and B are complementary.
At
, 


So

At
, 





The period,
, is related to
by

B. kinetic energy increases and potential energy decreases
Answer:
Density of 18.0-karat gold mixture is
.
Explanation:
A mixture of 18 parts gold, 5 parts silver, and 1 part copper.
Let mass of gold be 18x
Let the mass of silver be 5x
Let the mass of copper be 1x
The density of gold = 
The density of silver = 
The density of copper =

Volume of the gold in the mixture = 
Volume of the silver in the mixture = 
Volume of the copper in the mixture = 
Mass of the mixture = M = 18x+5x+1x =24x
Volume of the mixture = 
Density of the mixture:

You can solve this using the equation k=mv^2. k is the kinetic energy, m is the mass, and is the velocity. k=30(3.4)^2, so the answer is 346.8 J.