Question

REMARKS In evaluating the sine or cosine function, the angle is in radians, so you should either set your calculator to evaluate trigonometric functions based on radian measure or convert from radians to degrees.

QUESTION If the mass is doubled, is the magnitude of the acceleration of the system at any position doubled, halved, or unchanged?

doubled, halved, or unchanged?

PRACTICE IT

Use the worked example above to help you solve this problem.(a) Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following.

x = (0.270 m) cos( * t)

8.00

A =	_____ m
f =	_____ Hz
T =	_____ s

(b) Find the maximum magnitude of the velocity and acceleration.

vmax =	______ m/s
amax =	______ m/s2

(c) What are the position, velocity, and acceleration of the object after 1.20 s has elapsed?

x =	______ m
v =	______ m/s
a =	______ m/s2

EXERCISE

If the object-spring system is described by x = (0.345 m) cos (2.00t), find the following.(a) the amplitude, the angular frequency, the frequency, and the period

A =	______ m
? =	______ rad/s
f =	______ Hz
T =	______ s

(b) the maximum magnitudes of the velocity and the acceleration

vmax =	______ m/s
amax =	______ m/s2

(c) the position, velocity, and acceleration when t = 0.250 s

x =	______ m
v =	______ m/s
a =	______ m/s2

Answer 1

x = 0.270 cos(pi t / 8)

A = 0.280 m

w = 2 pi f = pi / 8

f = 0.0625 Hz

(B) Vmax = Aw = (0.270)(pi/8)

= 0.106 m/s

a_max = A w^2 = 0.042 m/s^2

(C) x = 0.270 cos(pi t / 8)

x = 0.24 m

v = 0.048 m/s

a = 0.0374 m/s^2

-----------------------Exrecixe

x = 0.345 cos(2t)

A = 0.345m

w = 2 pi f = 2 rad/s

f =0.318 Hz

(B) Vmax = Aw = (0.345)(2)

= 0.69 m/s

a_max = A w^2 = 1.38 m/s^2

(C) x = 0.345 cos( 2 t)

x = 0.303 m

v = 0.33 m/s

a = 1.21 m/s^2