How do I work this out

A body with mass of 200 g is attached to the end of a spring that is stretched 20 cm by a force of 9 N. At time tequals0 the bod

11Alexandr11 [23.1K]

Answer:

X(t) = 13/13 cos(12t+α)

C =13/13

π/6 s

Explanation:

(A) A body with mass 200 g is attached to the end of a spring that is stretched 20 cm by a force of 9 N. At time t = 0 the body is pulled 1 m in to the right, stretching the spring, 3 set in motion with an initial velocity of 5 m/s to the left.

(a) Find X(t) in the form c • cos(w_o*t— α)

(b) Find the amplitude 3 Period of motion of the body 1

mass: m = 200g = 0.200 kg

displacement: ΔX = 20 cm = 0.20 m

Spring Constant: K = 9/0.20 = 45 N/m

IV: X(0) = 1m V(0) = -5 m/s

Simple Harmonic Motion: c•cos(cosw_t— α) = X(t)

Circular Frequency: w_o = √k/m= √36/(0.20) = 13 rad/s

X(0) = 1m =c_1

X'(0) = V(0) = c_2*w_o/w_o

= -5/12 = c_2

"radians Technically Unitless"

Amplitude: c = √ci^2 + c^2 ==> √1^2 + (-5/12)^2 = 1 m =13/13 = c

X(t) = 13/13 cos(12t+α)

since, C>0 : damped forced vibration c_1>0, c_2>0

phase angle 2π+tan^-1(c_2/c_1)

=2π+tan^-1(-5/12/1)= 5.884

period: T =2π/w_o

=π/6 s

6 0

4 years ago

When talking about Acceleration ,what is significant about the about the sign(+ or -)?

OLEGan [10]

Answer:

Acceleration at its most basic is the act of increasing your running speed. From a standing start (or blocks), you explode into action. If you’re already running, you pick up the pace. Acceleration continues until you can no longer increase your speed, at which point you achieve maximum velocity (top-end speed). Acceleration seems simple enough. The plus means your increasing speed, the k=minus means your decreasing in speed.

Explanation:

5 0

3 years ago

An ice cube of volume 15 cm^3 and density 917 kg/m^3 is placed in ethyl alcohol of density 811 kg/m^3. What is the buoyant force

Amiraneli [1.4K]

Answer:

the buoyant force acting on the ice cube is 0.119 N

Explanation:

given,

volume of ice cube = 15 cm³ = 15 × 10⁻⁶ m³

density of ice cube = 917 kg/m³

density of ethyl alcohol = 811 kg/m³

buoyant force = ?

The density of ice is more than ethyl alcohol hence it will sink.

buoyant force acting on the ice cube = ρ V g

= 811 × 15 × 10⁻⁶ × 9.81

=0.119 N

so, the buoyant force acting on the ice cube is 0.119 N

3 0

3 years ago

The amount of work done by two boys who apply 200 N of force in an

Aleksandr [31]

The amount of work done by two boys who apply 200 N of force in an unsuccessful attempt to move a stalled car is 0.

Answer: Option B

<u>Explanation: </u>

Work done is the measure of work done by someone to push an object from its present position. We can also define work done as the amount of forces needed to move an object from its present position to another position. So the amount of work done is directly proportionate to the product of forces acting on the object and the displacement of the object.

$\text { Work done }=\text { Force } \times \text { displacement }$

So in this present case, as the two boys have done an unsuccessful attempts to push a stalled car so that means the displacement of the car is zero as there is no change in the position of the car. But they have applied a force of 200 N each. So the amount of work done will be

$\text { Work done }=200 \mathrm{N} \times 0=0$