1) On a horizontal, frictionless surface, a block of mass m = 4 kg is attached to a spring of spring constant 200 N/m. The block is observed to undergo simple harmonic motion. Answer the following: (a) What is the period of the oscillation? (b) How would the period change if the mass were quadrupled, assuming the spring constant remains the same?

2) Light travels from air into a rectangular slab of unknown material. The angle of incidence is 25 degrees, and the angle of refraction is 15 degrees. (a) Find the index of refraction of the rectangular slab, and (b) what is the velocity of light in the slab?

(1)  Ts?=0.8886seconds

Ts2?=2×Ts1?

(2) n=1.6329

v=1.8372×108m/s

Step-by-step explanation

1) Answer the following: (a) What is the period of the oscillation? (b) How would the period change if the mass were quadrupled, assuming the spring constant remains the same?

(a) PERIOD OF THE OSCILLATION, T_S

Ts?=2πkm??

where: m is the mass and k is the spring constant

To get the period of oscillation, just substitute the values to the equation above.

Ts?=2π200N/m4kg??=0.8886seconds

(b)  From the equation of the period of oscillation, let the    2π and k?  be constant since they are not change on the given problem.

Just the T_Sand m are the variables needed. 

Ts?=2πkm??→constant=m?Ts??

On the problem, the mass is quadrupled. 

m1??Ts1??=m2??Ts2??;m2?=4×m1?

Ts2?=Ts1?m1?m2???=Ts1?m1?4×m1???=4?×Ts1?=2×Ts1?

The period of oscillation is expected to be doubled if the mass were quadrupled. 

(2) (a) Find the index of refraction of the rectangular slab, and (b) what is the velocity of light in the slab?

(a) Index of refraction

n1?sin(θ1?)=n2?sin(θ2?)→Snell′sLaw

n2?=sin(θ2?)n1?sin(θ1?)?=sin(15)1×sin(25)?=1.6329

(b) Velocity of light

n=vc?;v=nc?

where n is the index of refraction

c is the speed of light (3 x 10^8 m/s)

v=nc?=1.63293×108m/s?=1.8372×108m/s